·
N. BELLOMO, A. PALCZEWSKI, G. TOSCANI
Mathematical Topics in Nonlinear Kinetic Theories, World Scientific, Singapore
(1988), pg. IX + 226
·
N. BELLOMO, M. LACHOWICZ, J. POLEWCZAK,
G. TOSCANI Mathematical Topics in Nonlinear Kinetic Theory II: The Enskog Equation, World Scientific, Singapore (1991), pg. X
+ 207
·
L. PARESCHI, G.
TOSCANI, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo
Methods, Oxford University Press, Oxford (2014), pg. XII + 376
·
G.
TOSCANI , V. BOFFI, S. RIONERO Eds.
Mathematical Aspects of Fluid and Plasma
Dynamics, Lecture Notes in Mathematics n.1460, Springer Verlag, Berlin
(1991), pg. 221
·
V.
BOFFI, F. BAMPI, G. TOSCANI Eds. Nonlinear Kinetic Theory and Mathematical Aspects of
Hyperbolic Systems, World Scientific, Singapore (1992) pg. XI + 267
·
G. TOSCANI, Guest Editor Transport
Theory and Statistical Physics Special
Issue devoted to the Proceedings of the Second International Workshop on
Nonlinear Kinetic Theories and Mathematical Aspects of Hyperbolic Systems 25 , n. 3-5 (1996) 263-592
·
L.
PARESCHI, G.RUSSO, G.TOSCANI Eds. Modelling
and Numerics of Kinetic Dissipative Systems, Nova
Science Publishers, New York, (2005) pg. II + 230
·
G.TOSCANI Ed. Kinetic Methods for Nonconservative and Reacting
Systems, QM n.16, Aracne Editrice,
Roma, (2005) pg. 331
· G.NALDI, L.PARESCHI, G.TOSCANI Eds. Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, Birkhauser, Boston (2010) pg. X + 435
· G. Martalò, G. Toscani, M. Zanella, Individual-based foundation of SIR-type epidemic models:mean-field limit and large time behaviour. (Preprint) (2025) Download
·
G.Auricchio, P.
Giudici, G. Toscani, The Gini index as a coefficient of variation.
In: di Bella, E., Gioia, V., Lagazio, C., Zaccarin, S. (eds) Statistics for Innovation II. SIS 2025. Italian
Statistical Society Series on Advances in Statistics. Springer, Cham.
·
G. Auricchio, P. Giudici, G. Toscani, A.E. Bernardelli, Measuring multivariate divergences
to improve neural network performances
(preprint (2025) Download
·
G. Auricchio, G. Loli, G. Toscani, Measuring inequality in high dimensions: A Gini based approach. Statistics (In press)
(2025) Download
·
G. Auricchio, G. Brigati, P. Giudici, G. Toscani, From kinetic theory to AI: a rediscovery
of high-dimensional divergences
and their properties.
(Preprint) (2025) Download
· M. Menale, G. Toscani, Measuring inequality in
society-oriented Lotka-Volterra-type kinetic equations. (Preprint) (2025) Download
·
G. Auricchio, P. Giudici, G. Toscani, How to measure
multidimensional variation?
(Preprint) (2024) Download
· G. Toscani, M. Zanella, Condensation effects in
kinetic models for consensus dynamics: finite-time blow-up and regularity
aspects. (Preprint) (2024) Download
· A. Bondesan, M. Menale, G. Toscani, M. Zanella,
Lotka-Volterra-type kinetic equations for interacting species. Nonlinearity,
(in press) (2025) Download
· G. Toscani. Measuring multidimensional heterogeneity
in emergent social phenomena. European Journal of Applied Mathematics, 36 (2)
316-327 (2025) Download
· P.
Giudici, E. Raffinetti, G. Toscani. Measuring multidimensional inequality: a new proposal
based on the Fourier transform. Statistics, 59 330-353 (2025) Download
·
G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Multivariate
Gini-type discrepancies.
Math. Models Methods Appl. Sci., 35 (5) 1267-1296
(2025) Download
· G. Auricchio, P. Giudici, G. Toscani, Extending the
Gini index to higher dimensions using whitening processes. Rend. Lincei Mat. Appl., 35, 511-528 (2024) Download
·
E. Calzola, G. Dimarco, G. Toscani, M.
Zanella. Emergence of condensation patterns in
kinetic equations for opinion dynamics. Physica D: Nonlinear Phenomena, 470, 134356 (2024) Download
· G.
Bertaglia, A. Bondesan, D. Burini, R. Eftimie, L.
Pareschi, G. Toscani. New trends
on the systems approach to modeling SARS-CoV-2 pandemics in a globally
connected planet. Math. Models Methods Appl. Sci. 34 (11) 1995-2054 (2024) Download
· G.
Bertaglia, L. Pareschi, G. Toscani. Modelling
contagious viral dynamics: a kinetic approach based on mutual utility. Mathematical
Biosciences and Engineering, 21 (3) 4241-4268 (2024) Download
·
G.
Toscani, M. Zanella, On a kinetic description of Lotka-Volterra dynamics.
Rivista Matematica Università di Parma,
15 (1) 61-77 (2024) Download
· A.
Bondesan, G. Toscani, M. Zanella. Kinetic
compartmental models driven by opinion dynamics: vaccine hesitancy and social
influence. Math. Models Methods Appl.
Sci. Vol. 34, (6), 1043-1076 (2024) Download
·
G.
Dimarco, G. Toscani, M. Zanella, A multi-agent description of the influence of
higher education on social stratification. Journal of Economic Interaction & Coordination 19 (3) 493-521 (2024) Download
· F. Auricchio, M. Carraturo, G. Toscani, M. Zanella,
Impact of interaction forces in first-order many-agent
systems for swarm manifacturing. Discrete and
Continuous Dynamical Systems - Series S, 17 (1) 78-97 (2024) Download
· F.
Auricchio, G. Toscani, M. Zanella, Trends to equilibrium for a nonlocal
Fokker-Planck equation. Applied Mathematics Letters, 145, 108746 (2023) Download
·
G. Toscani,
One-dimensional Barenblatt-type solutions and related
inequalities. Ricerche di Matematica
73 (Suppl.1) 309-321 (2023) Download
·
L. Pareschi, G. Toscani, The kinetic theory of mutation rates.
Axioms, 12; 265 (2023) Download
·
G.
Toscani, A multi-agent description of social phenomena with lognormal
equilibria. In P. Barbante et al. (eds.), From Kinetic Theory to Turbulence Modeling,
Springer INdAM Series 51, Springer Nature, Singapore.
pp. 261-270 (2023) Download
·
F. Auricchio, G. Toscani, M. Zanella,
Fokker-Planck modeling of many-agent systems in swarm manifacturing:
asymptotic analysis and numerical methods. Commun. Math. Sci. 21 (6) 1655-1677
(2023) Download
·
S.
Gualandi, G. Toscani, E. Vercesi, A kinetic description of the body size
distributions of species. Math. Models Methods Appl. Sci. 32 (14) 2853–2885 (2022) Download
·
G.Toscani, A multi-agent approach to the impact of epidemic spreading on
commercial activities. Math. Models Methods Appl. Sci. 32 (10) 1931-1948 (2022)
Download
·
G.
Toscani, On Fourier-based inequality measures. Entropy 24; 1393 (2022) Download
·
G. Toscani,
P. Sen, S. Biswas, Kinetic exchange models of societies and economies. Phil.
Trans. R. Soc. A 380, 20210170 (2022) Download
·
E.
Bernardi, L. Pareschi, G. Toscani, M. Zanella, Effects of vaccination efficacy on
wealth distribution in kinetic epidemic models. Entropy, 24; 216
(2022) Download
·
G. Albi, G. Bertaglia, W. Boscheri, G. Dimarco, L. Pareschi, G.
Toscani, M. Zanella. Kinetic
modelling of epidemic dynamics: social contacts, control with uncertain data,
and multiscale spatial dynamics. pp. 43-108 In:
Bellomo, N., Chaplain, M.A.J. (eds) Predicting
Pandemics in a Globally Connected World, Volume 1. Modeling and Simulation
in Science, Engineering and Technology. Birkhäuser,
Cham 2022 Download
·
G.
Dimarco, G. Toscani, M. Zanella, Optimal control of epidemic spreading in
presence of social heterogeneity. Phil. Trans. R. Soc. A 380, 20210160 (2022) Download
·
G. Furioli, A. Pulvirenti, E. Terraneo,
G. Toscani, Fokker-Planck equations and one-dimensional functional inequalities
for heavy tailed densities, Milan J. Math., 90, 177–208 (2022) Download
· L.
Pareschi, G. Toscani, Dinamiche sociali ed equazioni alle derivate parziali in
ambito epidemiologico. Matematica Cultura e Società, Serie I, Vol. 6 n.3 (2021) Download
· G. Toscani, M. Zanella, On a class of Fokker-Planck
equations with subcritical confinement. Rend. Lincei
Mat. Appl. 32 (3) 471-497 (2021) Download
·
M.Azzi, C. Bardelli, S.
Deandrea, G. Dimarco, S. Figini,
P. Perotti, G. Toscani, M. Zanella, A data-driven epidemic model with social
structure for understanding the COVID-19 infection on a heavily affected
Italian Province. Math. Models Methods Appl. Sci. 31 (12) 2533-2570 (2021) Download
·
M.
Zanella, C. Bardelli, M.Azzi,
S. Deandrea, P. Perotti, S. Silva, E. Cadum, S. Figini,
G. Toscani, Social contacts, epidemic spreading and health system. Mathematical
modeling and applications to COVID-19 infection, Mathematical Biosciences and Engineeering, 18 (4) 3384-3403 (2021)
Download
· G. Toscani, Entropy-type inequalities for generalized
Gamma densities. Ricerche di Matematica,
70, 35-50 (2021) Download
· L. Preziosi, G. Toscani, M. Zanella, Control of tumour growth distributions through kinetic methods.
Journal of Theoretical Biology 514, 110579 (2021)
Download
·
G.
Dimarco, B. Perthame, G. Toscani, M. Zanella, Kinetic
models for epidemic dynamics with social heterogeneity. Journal of Mathematical
Biology, 83 n. 4 (2021) Download
·
G.
Toscani, Statistical description of human addiction phenomena. In Trails in
Kinetic Theory: foundational aspects and numerical methods, A. Nota, G.
Albi, S. Merino-Aceituno, M. Zanella Eds, SEMA SIMAI Springer Series Vol. 25,
209-226 (2021) Download
·
E. Ballante, C. Bardelli, M.
Zanella, S. Figini, G. Toscani. Economic
Segregation Under the Action of Trading Uncertainties, Symmetry, 12, 1390
(2020) Download
· G.
Auricchio, A. Codegoni, S. Gualandi, G. Toscani, M.
Veneroni. On the equivalence between Fourier-based
and Wasserstein metrics. Rend. Lincei Mat. Appl. 31,
627-649 (2020) Download
· G. Dimarco, L.Pareschi,
G. Toscani, M. Zanella, Wealth distribution under the spread of infectious
diseases. Phys. Rev. E, 102, 022303 (2020) Download
· G.
Dimarco, G. Toscani, Social climbing and Amoroso distribution.
Math. Models Methods Appl. Sci. 30 (11)
2229-2262 (2020) Download
· G. Toscani, A. Tosin, M. Zanella, Kinetic modelling of
multiple interactions in socio-economic systems. Netw.
Heterog. Media, 15, (3) 519-542 (2020) Download
· G. Furioli, A. Pulvirenti,
E. Terraneo, G. Toscani, Non-Maxwellian kinetic
equations modeling the evolution of wealth distribution. Math. Models Methods
Appl. Sci. 30 (4) 685-725 (2020) Download
· G. Furioli, A. Pulvirenti,
E. Terraneo, G. Toscani, Wright-Fisher-type equations
for opinion formation, large time behavior and weighted logarithmic-Sobolev
inequalities. Ann. IHP, Analyse Non Linéaire 36, 2065-2082 (2019) Download
· G. Toscani, A. Tosin, M. Zanella, Multiple-interaction
kinetic modelling of a virtual-item gambling economy. Phys. Rev. E, 100, 012308
(2019) Download
· G. Dimarco, G. Toscani, Kinetic modeling of alcohol
consumption. J. Stat. Phys. 177,1022–1042 (2019) Download
·
L. Pareschi, G. Toscani, A. Tosin, M. Zanella, Hydrodynamics
models of preference formation in multi-agent societies. J. Nonlinear Science,
29 (6), 2761-2796 (2019) Download
· G.Toscani, The information-theoretic meaning of
Gagliardo-Nirenberg type inequalities. Rend. Lincei
Mat. Appl. 30, 237–253 (2019) Download
· S. Gualandi, G. Toscani, Human behavior and lognormal
distribution. A kinetic description. Math. Models Methods Appl. Sci. 29, (4)
717-753 (2019) Download
· S. Gualandi, G. Toscani, The size distribution of
cities: A kinetic explanation. Physica A, 524, 221-234 (2019) Download
· G. Toscani, Poincaré-type
inequalities for stable densities. Ricerche Mat. 68
(1) 225–236 (2019) Download
· G. Toscani, A. Tosin, M. Zanella, Opinion modeling on
social media and marketing aspects, Phys. Rev. E,
98, 022315 (2018) Download
· B. Duering, L. Pareschi, G.
Toscani, Kinetic models for optimal control of wealth inequalities. Eur. Phys.
J. B 91: 265 (2018) Download
· S. Gualandi, G. Toscani, Call center service times are
lognormal. A Fokker--Planck description. Math. Models Methods Appl. Sci. 28,
(08) 1513-1527 (2018) Download
· S.
Gualandi, G. Toscani, Pareto tails in socio-economic phenomena: A kinetic description. Economics: The Open-Access, Open-Assessment E-Journal, 12 (2018-31): 1–17. Download
·
C. Brugna, G.Toscani, Kinetic models
for goods exchange in a multi-agent market, Physica A 499 362–375 (2018) Download
· M. Torregrossa, G.Toscani,
Wealth distribution in presence of debts. A Fokker-Planck description, Commun.
Math. Sci. 16 (2) 537-560 (2018) Download
· G. Toscani, A Rosenau-type approach to the
approximation of the linear Fokker-Planck equation, Kinet. Relat.
Models 11 (4)697-714 (2018) Download
· M. Torregrossa, G.Toscani,
On a Fokker-Planck equation for wealth distribution, Kinet. Relat.
Models 11(2)337-355 (2018) Download
· G.Toscani, Continuum models in wealth distribution, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.28 451–461 (2017) Download
·
G.
Toscani, Score functions, generalized relative Fisher information and
applications, Ricerche mat. 66 15-26 (2017) Download
· G. Furioli, A. Pulvirenti,
E. Terraneo, G. Toscani, Fokker--Planck equations in
the modelling of socio-economic phenomena, Math. Models Methods Appl. Scie. 27
(1) 115-158 (2017) Download
· G. Albi, L. Pareschi, G.
Toscani, M. Zanella, Recent advances in opinion modeling: Control and social
influence. In “Active Particles, Volume 1: Theory, Models, Applications” N.
Bellomo, P. Degond, E. Tadmor, Eds. Ch.2, pp. 49-98. Birkhäuser Boston (2017) Download
·
G.
Toscani, Diffusion equations and entropy inequalities, (Lectures at Ravello’s
School) (2016) Download
· G. Toscani, Kinetic and mean field description of Gibrat’s law. Physica A, 461 802-811 (2016) Download
· G.
Toscani, Sulle code di potenza di Pareto, La Matematica nella Società e nella
Cultura, Serie I, 1 21-30 (2016) Download
· G. Toscani, Entropy inequalities for stable densities
and strengthened central limit theorems, J. Stat. Phys., 165 371–389 (2016) Download
·
G.Toscani, The
fractional Fisher information and the central limit theorem for stable laws, Ricerche Mat., 65 (1) 71-91 (2016) Download
· J. Dolbeault, G. Toscani,
Nonlinear diffusions: extremal properties of Barenblatt
profiles, best matching and delays, NonlinearAnal.
Series A,138 31-43 (2016) Download
· J.A.
Carrillo, M. Di Francesco, G. Toscani, Condensation phenomena in nonlinear drift equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XV
145-171 (2016) Download
· C. Brugna, G. Toscani,
Kinetic models of opinion formation in the presence of personal conviction,
Phys. Rev. E92, 052818 (2015) Download
·
G.
Toscani, A strengthened entropy power inequality for log-concave densities,
IEEE Transactions on Information Theory 61 (12) 6550-6559 (2015) Download
· J. Dolbeault, G. Toscani,
Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities,
Int. Math. Res. Notices rnv 131 (2015) Download
· F. Bassetti, G. Toscani, Mean field dynamics of
collisional processes with duplication, loss and copy, Math. Mod. Meth. Appl.
Sci. 25 (10) 1887-1925 (2015) Download
· C. Brugna, G. Toscani,
Boltzmann-type models for price formation in the presence of behavioral
aspects, Netw. Heterog. Media 10 (3) 543-557 (2015) Download
·
G.
Toscani, A concavity property for the reciprocal of Fisher information and its
consequences on Costa's EPI, Physica A, 432 35-42 (2015) Download
· G. Furioli, A. Pulvirenti,
E. Terraneo, G. Toscani, On Rosenau-Type
approximations to fractional diffusion equations, Commun. Math. Sci. 13 (5)
1163-1191 (2015) Download
· J. Dolbeault, G. Toscani, Best matching Barenblatt profiles
are delayed, J. Phys. A: Math. Theor. 48 065206 (2015) Download
·
J.A.
Carrillo, G. Toscani, Renyi entropy and improved
equilibration rates to self-similarity for nonlinear diffusion equations,
Nonlinearity, 27, 3159-3177 (2014) Download
·
F.
Bassetti, G. Toscani, Explicit equilibria in bilinear kinetic models, Esaim: Proceedings and Surveys, 47 1-16 (2014) Download
·
L. Pareschi, G. Toscani, Wealth distribution and collective
knowledge. A Boltzmann approach, Phil. Trans. R. Soc. A 372, 20130396, 6
October (2014) Download
· G. Toscani, Rényi entropies and nonlinear diffusion
equations, Acta. Appl. Math., 132 595–604 (2014) Download
·
G.
Toscani, Heat equation and convolution inequalities, Milan J. Math., 82 (2)
183-212 (2014)
·
G. Savaré,
G. Toscani, The concavity of Renyi entropy power,
IEEE Transactions on Information Theory, 60 (5) 2687-2693 (2014) Download
· G. Toscani, A kinetic description of mutation
processes in bacteria, Kinet. Relat. Models, 6 (4)
1043-1055 (2013) Download
· T. Rey, G. Toscani, Large-time behavior of the
solutions to Rosenau type approximations to the heat equation, SIAM J. Appl.
Math. 73 (4), 1416-1438 (2013) Download
·
G.
Toscani, C. Brugna, S. Demichelis, Kinetic models for
the trading of goods, J Stat Phys, 151, (2013) 549-566 Download
·
J. Dolbeault, G. Toscani, Improved interpolation inequalities,
relative entropy and fast diffusion equations, Ann. I.H. Poincaré
– AN, 30 (5) 917-934 (2013) Download
· G. Toscani, An
information-theoretic proof of Nash's inequality, Rend. Lincei Mat. Appl., 24, (2013) 83-93 Download
· G. Toscani, Lyapunov functionals for the heat equation
and sharp inequalities, Atti Acc. Peloritana Pericolanti, Classe Sc.
Fis. Mat. e Nat., 91, 1-10, (2013) Download
· D. Matthes, G. Toscani, Variation on a theme by
Bobylev and Villani, C.R.Acad.Sci. Paris, Ser. I, 350
(1-2) (2012) 107-110 Download
· G. Furioli, A. Pulvirenti, E. Terraneo, G. Toscani, The
grazing collision limit of
the inelastic Kac model around a Lévy-type equilibrium. SIAM J. Math. Anal.
44, 827-850 (2012) Download
· G. Toscani, Finite time blow up in Kaniadakis-Quarati
model of Bose-Einstein particles. Comm. Part. Diff. Eqns. 37 (1) (2012) 77-87 Download
·
S.
Fornaro, S. Lisini, G. Savaré, G. Toscani, Measure
valued solutions of sub-linear diffusion equations with a drift term, Discrete
and Continuous Dynamical Systems A., 32 (5) 1675-1707 (2012) Download
· G. Toscani, N. Ben Abdallah, I. M. Gamba,
On the minimization problem of sub-linear convex functionals. Kinetic and related Models,
4 (4), (2011) 857-871 Download
· J. Dolbeault, G. Toscani,
Fast diffusion equations: Matching large time asymptotics
by relative entropy methods. Kinetic and related Models 4 (2011) 701-716 Download
· F. Bassetti, L. Ladelli, G.
Toscani: Kinetic models with randomly perturbed binary collisions. J. Statist. Phys. 142 (4) (2011) 686-709 Download
·
T.
Allemand, G. Toscani, The grazing collision limit of Kac caricature of
Bose-Einstein particles, Asymptotic Analysis, 72 (3-4) (2011) 201-229 Download
· D. Matthes, A. Juengel, G.Toscani, Convex Sobolev inequalities derived from
entropy dissipation, Arch. Rat. Mech. Anal.
199 (2) (2011) 563-596 Download
·
M. Fornasier, J. Haskovec, G. Toscani, Fluid dynamic
description of flocking via Povzner–Boltzmann
equation, Physica D 240 (2011) 21-31 Download
· F.
Bassetti, G. Toscani, Explicit equilibria in a kinetic model of gambling, Phys. Rev. E, 81, 066115 (2010) Download
· J. A. Carrillo, M. Fornasier,
G. Toscani, F. Vecil, Particle, Kinetic, and
Hydrodynamic Models of Swarming, in Mathematical Modeling of Collective
Behavior in Socio-Economic and Life Sciences, G. Naldi, L. Pareschi
and G. Toscani Eds. Birkhauser, Boston
(2010) 297-336 Download
·
D.
Matthes, G. Toscani, Propagation of Sobolev regularity for a class of random
kinetic models on the real line, Nonlinearity 23 (2010) 2081-2100 Download
· R. Duan, M. Fornasier, G.
Toscani, A kinetic flocking model with diffusion, Commun. Math. Phys. 300, (2010) 95–145 Download
· C. Brugna, G. Toscani,
Wealth redistribution in Boltzmann-like models of conservative economies, in Econophysics & Economics of Games, Social Choices and
Quantitative Techniques, B. Basu, B.K. Chackabarti,
S.R. Chackavarty, K. Gangopadhyay (Eds.) Springer Verlag, Milan (2010) 71-82 Download
·
G. Furioli, A. Pulvirenti, E. Terraneo,
G. Toscani, Convergence to self-similarity for the Boltzmann equation for
strongly inelastic Maxwell molecules, Annales de l'Institut
Henri Poincaré (C) Analyse Non Linéaire,
27, (2) (2010) 719-737 Download
· J.A. Carrillo, M. Fornasier,
J. Rosado, G. Toscani, Asymptotic flocking dynamics for the kinetic Cucker-Smale model, SIAM J. Math. Anal. 42, (1) (2010). 218-236 Download
·
G.
Toscani, Wealth redistribution in conservative linear kinetic models with
taxation, Europhysics Letters 88 (1) (2009) 10007 Download
· M. Bisi, G. Spiga, G. Toscani, Kinetic models of
conservative economies with wealth redistribution, Commun. Math. Sci.
7 (4) (2009) 901-916 Download
· B. Duering, D. Matthes, G.Toscani, A Boltzmann-type approach to the formation
of wealth distribution curves, (Notes of the Porto Ercole School, June 2008)
Riv. Mat. Univ. Parma (1) 8 (2009) 199-261 Download
· G. Furioli, A. Pulvirenti,
E. Terraneo, G. Toscani, Strong Convergence towards
self-similarity for one-dimensional dissipative Maxwell models, J. Funct. Anal. 257 (7)
(2009) 2291-2324 Download
·
V. Comincioli, L. Della Croce, G. Toscani, A Boltzmann-like
equation for choice formation, Kinetic and related Models 2 (1) (2009) 135- 149
Download
·
J.A.
Carrillo, S. Cordier, G. Toscani, Over-populated tails for
conservative-in-the-mean inelastic Maxwell models, Discrete and Continuous
Dynamical Systems A. 24 (1) (2009) 59-81 Download
·
F. Salvarani, G. Toscani, The diffusive limit of Carleman-type models in the range of very fast diffusion
equations, J.Evol.Equ. 9
(2009) 67-80 Download
· B. Duering, G.Toscani,
International and domestic trading and wealth distribution, Commun. Math. Sci.
6 (4) (2008) 1043-1058 Download
· B. Duering, D. Matthes, G.Toscani,
Kinetic Equations modelling Wealth Redistribution: A comparison of Approaches,
Phys. Rev. E, 78, (2008) 056103 Download
·
M. Bisi,
G. Spiga, G. Toscani, On the hydrodynamic closure of a transport-diffusion
equation, Europhysics Letters 83, (2008) 40007 Download
·
B. Lods,
C. Mouhot, G. Toscani, Relaxation rate, diffusion approximation and Fick's law
for inelastic scattering Boltzmann models, Kinetic and related Models, 2 (2008)
223-248 Download
·
B.
Duering, D. Matthes, G.Toscani, Exponential and
algebraic relaxation in kinetic models for wealth distribution, in Proceedings
WASCOM 2007 N. Manganaro, R. Monaco, S. Rionero Eds.,
World Scientific, Singapore 2008, 228-238 Download
· G.
Toscani, Funzionali entropia ed equilibrio di sistemi di molte particelle,
Bollettino UMI serie IX, Vol. 1 (3) (2008), 509-524 Download
·
G.
Toscani, Hydrodynamics from the dissipative Boltzmann equation, in
"Mathematical models of granular matters" G. Capriz,
P. Giovine and P. M. Mariano Editors, Lecture Notes in Mathematics n.1937
(2008) 59-75 Download
· U. Gianazza, G. Savaré, G. Toscani, The Wasserstein
gradient flow of the Fisher information and the quantum drift-diffusion
equation, Arch. Rat. Mech. Anal. 194, (1) (2009) 133-220 Download
·
D.
Matthes, G.Toscani, Analysis
of a model for wealth redistribution, Kinetic and related Models, 1 (2008),
1-22 Download
· D. Matthes, G. Toscani, On steady distributions of
kinetic models of conservative economies, J. Statist. Phys., 130 (2008) 1087-1117 Download
· J.A. Carrillo, G. Toscani, Contractive probability
metrics ans asymptotic behavior of dissipative
kinetic equations (Notes of the Porto Ercole School, June 2006) Riv. Mat. Univ.
Parma, (7) 6, (2007) 75-198 Download
· J.A. Carrillo, M. Di Francesco, G. Toscani, Strict Contractivity of the 2-Wasserstein distance for the porous
medium equation by mass-centering, Proc. Amer. Math. Soc.
135 (2007), 353-363 Download
·
B.
Duering, G. Toscani, Hydrodynamics from kinetic models of conservative
economies, Physica A: Statistical Mechanics and its Applications, 384 (2007)
493-506 Download
· M.J. Càceres, G. Toscani,
Kinetic approach to long time behavior of linearized fast diffusion equations,
J. Statist. Phys., 128 (4) (2007) 883-925 Download
·
G. Aletti,
G. Naldi, G. Toscani, First-order continuous models of opinion formation, SIAM
J. Appl. Math., 67 (3) (2007) 837-853 Download
· G. Toscani, Kinetic models of opinion formation,
Commun. Math. Sci. 4 (3) (2006) 481-496 Download
·
M. Bisi,
J.A. Carrillo, G. Toscani, Decay rates in probability metrics towards
homogeneous cooling states for the inelastic Maxwell model, J. Statist.Phys., 124 (2-4) (2006) 625-653 Download
· L. Pareschi, G. Toscani,
Self-similarity and power-like tails in nonconservative kinetic models, J.
Statist. Phys. 124 (2-4) (2006) 747-779 Download
· L. Gosse, G. Toscani, Lagrangian numerical approximations to one-dimensional convolution-diffusion
equations, SIAM J. Sci. Comput.,
28 (4) (2006) 1203-1227 Download
· M.P.Gualdani, A. Juengel, G.Toscani,
A nonlinear fourth-order parabolic equation with nonhomogeneous boundary
conditions, SIAM J. Math. Anal., 37 (6)
(2006) 1761-1779 Download
· L. Gosse, G. Toscani, Identification of asymptotic
decay to self-similarity for one-dimensional filtration equations, SIAM J. Numer. Anal., 43 (6)
(2006) 2590-2606 Download
· J.A. Carrillo, M. Di Francesco, G. Toscani,
Intermediate asymptotics beyond homogeneity and
self-similarity: long time behavior for nonlinear diffusions, Arch. Ration. Mech. Anal., 180 (1) (2006) 127-149 Download
·
S.
Cordier, L. Pareschi, G. Toscani, On a kinetic model
for a simple market economy, J. Statist. Phys., 120 (2005) 253-277 Download
· M.J. Càceres, J.A. Carrillo,
G.Toscani, Long-time
behavior for a nonlinear fourth order parabolic equation, Trans. Amer.
Math. Soc. 357 (2005) 1161-1175 Download
· M. Bisi,
J.A. Carrillo, G. Toscani, Contractive Metrics for a Boltzmann equation
for granular gases: Diffusive equilibria,
J. Statist. Phys., 118
(1-2) (2005) 301-331 Download
· F. Filbet, L. Pareschi, G. Toscani, Accurate numerical methods for the
collisional motion of (heated) granular flows, J. Comput. Phys. 202, (1) ( 2005) 216-235 Download
·
B. Lods,
G. Toscani, Long time behavior of non--autonomous
Fokker--Planck equations and the cooling of granular gases., Ukrainian Math.
J., 57 (6) 778-789 (2005) Download
· F. Salvarani, G. Toscani,
Large-time asymptotics for nonlinear diffusions: the
initial-boundary value problem, J. Math. Phys. 46,
023502 (2005) (11 pages) Download
·
G.
Toscani, A central limit theorem for solutions of the porous medium equation,
J. Evol. Equ. 5 (2005) 185-203 Download
· J.A. Carrillo, G. Toscani, Wasserstein metric and
large-time asymptotics of nonlinear diffusion
equations, in New trends in mathematical physics,
World Sci. Publ., Hackensack, NJ, (2004) 234–244.
Download
Old Papers
1. F.Barbaini, G.Toscani, Costruzione di misure mediante tempi
d'arresto, Rend. Ist. Lombardo, 1(A) 109, (1975)
49-64
2. I.Guarneri, G.Toscani, Statistical equilibrium
of a classical, randomly driven radiating system, Lett.Nuovo Cimento 14, n.3, serie 2 (1975) 101-107
3. I.Guarneri, G.Toscani, Stochastic electrodynamics of a one-dimensional
cavity, Bollettino UMI 1(5) 14-B (1977) 31-41
4. C.Bertoluzza, G.Toscani, Caratterizzazione della legge di
composizione d'esperienza per misure d'informazione idempotenti, Rend. Ist. Lombardo 1(A) 112 (1978) 99-109
5. C.Bertoluzza, G.Toscani, Diramativit`a
generalizzata e leggi di composizione in teoria dell'informazione, Rend. Ist. Lombardo 1(A) 113 (1979) 84-91
6. E.Gabetta, G.Toscani, Multiple random scattering in one dimension, Bollettino UMI 1(5) 17-B (1980) 1047-1062
7. G.Toscani, An approach to white-noise via wide-sense stationary
processes with piecewise constant sample functions, Bollettino UMI 118-A (1981)
309-315
8. E.Gabetta, G.Toscani,
Stochastic stability of a class of linear dynamical systems, Rend. Sem. Mat.Univ. Polit. Torino 40 (2) (1981) 53-62
9. G.Toscani, Products of independent random processes and
gaussian white-noise, Rend. Sem. Mat.Univ.
Polit. Torino, Special Issue (1982) 233-239
10. G.Toscani, Sums of independent random processes, Bollettino UMI
1(6) 1-A (1982) 241-248
11. G.Toscani, Random motion of a perfectly inelastic particle,
Atti VI Congr. Naz. AIMETA, Genova (1982), 1,
268-276
12. G.Toscani, Solution globale du modele a vitesse
discrète de l'équation de
Boltzmann en théorie cinetique,
C.R.A.S. t.296 Serie 1 (1983) 577-580
13. G.Toscani, On the discrete velocity models of the Boltzmann
equation in several dimensions, Ann.Matem. Pura Appl.
Vol.CXXXVIII (1984) 279-308
14. N.Bellomo, R.Illner, G.Toscani,
Sur le problème de Cauchy pour l'équation
de Boltzmann semi-discrète, C.R.A.S. t.299, Serie I
(1984) 835-839
15. G.Toscani, On the semidiscrete
Boltzmann equation, Atti VII Congr. Naz. AIMETA,
Trieste (1984), 1, 85-89
16. N.Bellomo, G.Toscani,
On the Cauchy problem for the nonlinear Boltzmann equation:global existence,uniqueness,
and asymptotic behaviour, J. Math.Phys.
12 (1985) 340-345
17. G.Toscani, On the asymptotic behaviour
and stability of the solution for the Broadwell model of the Boltzmann equation
in three dimensions, Math.Meth. in Appl. Sc. 17
(1985) 340-345
18. G.Toscani, Diffusion with collision of a perfectly inelastic
particle, Bollettino UMI 1(6) 4-B (1985) 801-812
19. G.Toscani, Global existence and asymptotic behaviour
for the discrete velocity models of the Boltzmann equation, J. Math.Phys. 111 (1985) 2918-2921
20. G.Toscani, N.Bellomo
Global existence, uniqueness and stability of the nonlinear Boltzmann equation
with almost general gas-particle interaction potential, Rend.Circolo
Matem. Palermo, Suppl. Serie II, n.8 (1985) 419-433
21. G.Toscani, The semidiscrete Boltzmann
equation for hard-spheres, Meccanica 120 (1985) 249-252
22. G.Toscani, Global existence and asymptotic behaviour
for the discrete velocity models of the Boltzmann equation, Quaderni
del CNR, GNFM Proceedings of Workshop on Mathematical Aspects of Fluid and
Plasma Dynamics, C.Cercignani,
S.Rionero, M.Tessarotto Eds., (1985) 565-573
23. N.Bellomo, G.Toscani,
On the Cauchy problem for the nonlinear Boltzmann equation: global existence,
uniqueness and asymptotic stability, Quaderni del
CNR, GNFM Proceedings of Workshop on Mathematical Aspects of Fluid and Plasma
Dynamics, C.Cercignani, S.Rionero, M.Tessarotto Eds., (1985) 45-60
24. G.Toscani, On the nonlinear Boltzmann equation in unbounded
domains, Arch.Ration. Mech. Anal. 195 (1986) 37-49
25. V.Protopopescu, G.Toscani, Existence
globale pour un problème mixte
associè á l'équation de
Boltzmann non-lineaire, C.R.A.S. t.302 Serie I, n.6
(1986) 255-258
26. N.Bellomo, G.Toscani,
The nonlinear Boltzmann equation: analysis of the influence of the cut-off on
the solution of the Cauchy problem, XV Int. Symposium on R.G.D., B.G.Teubner Editor Vol.I (1986) 167-174
27. N.Bellomo, G.Toscani,
Lecture notes on the Cauchy problem for the nonlinear Boltzmann equation,
Internal Report Dip.Matem. Polit. Torino, Levrotto & Bella Editors (1986) 1-101
28. G.Toscani, New results on the Boltzmann equation in unbounded
domains, Trans.Theory and Stat. Phys. 116 (2-3)
(1987) 223-230
29. N.Bellomo, G.Toscani,
On theEnskog-Boltzmann equation in the whole space
R3: Some global existence,uniqueness
and stability results, Comput.Math. Applic. 13 n.9-11 (1987) 851-859
30. G.Toscani, V.Protopopescu,
The nonlinear Boltzmann equation with partially absorbing boundary conditions.Global existence and
uniqueness results, J. Math. Phys. 128 (1987) 1140-1145
31. G.Toscani, H-theorem and asymptotic trend to equilibrium for a
rarefied gas in the vacuum, Arch.Ration. Mech.
Anal.100 (1987) 1-12
32. R.Monaco, G.Toscani,
New results on the semidiscrete Boltzmann equation
for a binary gas mixture, Meccanica 122 (1987) 179-184
33. G.Toscani, Global solutions to the Boltzmann equation near a
local Maxwellian, Rend. Sem. Mat.Univ. Pol. Torino, Fasc.Spec. Hyperbolic Equations (1988) 279-286
34. G.Toscani, C.V.M.Vandermee
An abstract approach to nonlinear Boltzmann type equations, Ann.Univ.
Ferrara Sez.7, Vol. XXXIV (1988) 75-100
35. G.Toscani, Global solutions of the initial value problem for
the Boltzmann equation near a local Maxwellian, Arch.Ration.
Mech. Anal. 102 (1988) 231-241
36. G.Toscani, On the Cauchy problem for the discrete Boltzmann
equation with initial values in L1( R+), Commun.Math. Phys. 1121 (1989) 121-142
37. N.Bellomo, G.Toscani,
On the Enskog-Boltzmann equation in unbounded
domains: some global existence and stability results Proceedings of III Meeting
on Waves and Stability in Continuous Media, Bari, 1985 M.Maiellaro, L.Palese
Eds., Bari (1989) 1-18
38. A.Palczewski, G.Toscani,
Global solution of the Boltzmann equation for rigid spheres and initial data
close to a local Maxwellian, J. Math.Phys. 430 (1989)
2445-2450
39. N.Bellomo, M.Lachowicz,
A.Palczewski, G.Toscani, On the initial value
problem for the Boltzmann equation with a force term, Trans.Theory
& Stat. Phys. 118 (1) (1989) 87-102
40. G.Toscani, Recent developments on the existence theory for the
discrete velocity models, Proceedings of Discrete Kinetic Theory, Lattice Gas
Dynamics and Foundation of Hydrodynamics, Torino, 1988, R.Monaco Ed.World
Scientific, Singapore (1989) 355-370
41. N.Bellomo, G.Toscani,
On the Cauchy problem for the discrete Boltzmann equation with multiple
collisions: existence, uniqueness and stability, Stab.Meth.
Appl. Anal. in Continua 1 (1990) 165-184
42. G.Borgioli, R.Monaco,
G.Toscani, On the semidiscrete Enskog equation,
Proceedings of the V Meeting on Waves and Stability in Continuous Media,
Sorrento, 1989, S.Rionero Ed.World Scientific, Singapore
(1991) 34-40
43. G.Borgioli, A.Pulvirenti,
G.Toscani, On the Cauchy
problem for the semidiscrete Enskog
equation, Proceedings of Advances in Kinetic Theory and Continuoum
Mechanics, R.Gatignol & Soubbaramayer Eds., Springer Verlag, Berlin (1991) 91-98
44. G.Toscani, W.Walus,
Recent results on the fractional step method in discrete kinetic theory,
Proceedings of Discrete Models od Fluid Dynamics,
Coimbra 1990, A.Alves Ed.,
World Scientific, Singapore (1991) 123-130
45. G.Toscani, Existence results for some nonlinear hyperbolic
system from kinetic theory of gases, Non
linear hyperbolic equations and field theory, M.K.V.Murthy& L.Spagnolo
Eds.(1991) Pitman Research Note Series
46. G.Toscani, On the discrete Boltzmann equation with multiple
collisions, Atti Accad.Peloritana Pericolanti, Classe
Sci. Fis. Mat. Nat. V. LXVIII, Suppl. 1 (1991) 441-457
47. G.Toscani, W.Walus,
The initial-boundary value problem for the four velocity
plane Broadwell model, Math.Meth. and Models in Appl.
Sci. 1 (1991) 293-310
48. G.Toscani, On Shannon's entropy powers inequality, Ann.Univ. Ferrara, Sez. 7, Vol. XXXVII (1991) 167--184
49. G.Toscani, An inequality for convex functionals and its
application to a Maxwellian gas Le Matematiche, XLVI,
1 (1991) 481 491
50. G.Toscani, Convergence towards equilibrium for a gas of
Maxwellian pseudomolecules, Cont.Mech. Termodyn. 4 (1992) 95-107
51. G.Toscani, New a priori estimates for the spatially homogeneous
Boltzmann equation, Cont.Mech. Termodyn.
4 (1992) 81-93
52. G.Toscani, A.V.Bobylev
On the generalization of the Boltzmann H-theorem for a
spatially homogeneous Maxwell gas, J. Math.Phys. 33
(1992), 2578--2586.
53. G.Toscani, Lyapunov functionals for a Maxwell gas, Arch.Ration. Mech. Anal. 119 (1992) 301-307
54. V.Comincioli, G.Toscani,
Operator splitting of the Boltmann equation for a
Maxwell gas in “Boundary Value Problems for Partial Differential Equations and
Applications”, RMA Res. Notes Appl. Math., 29 C.Baiocchi and J.L.Lions Eds., Masson Paris, (1993) 345--350
55. E.Gabetta, G.Toscani,
On convergence to equilibrium for Kac's caricature of a Maxwellian gas, J. Math.Phys. 35, 1 (1994) 190-208
56. E.Gabetta, G.Toscani,
On entropy production rates for some kinetic equations, Bull.Tech.
Univ. Istanbul 47, (1994) 219-230
57. G.Toscani, Bivariate
distributions with given marginals and applications to kinetic theory of gases, Atti
"Convegno Nazionale del Gruppo AIMETA di Meccanica Stocastica'' E.
Mascolino Ed., Messina (1994)
58. G.Toscani, Strong convergence in Lp
for a spatially homogeneous Maxwell gas with cut-off, Transp.The.& Stat. Phys.
26 (1995) 319-328
59. P.L.Lions, G.Toscani,
A sthrenghtened central limit theorem for smooth
densities, J. Funct.Anal. 128 (1995) 148-167
60. V.Comincioli, G.Naldi,
G.Toscani, Nonlinear
diffusion and fluid dynamical limit from discrete velocity models, Comm. Appl.
Nonlinear Anal. 2 (1995) 1-29
61. E.Gabetta, G.Toscani,
B.Wennberg Metrics for
probability distributions and the trend to equilibrium for solutions of the
Boltzmann equation J. Statist.Phys. 81 (1995) 901-934
62. A.Pulvirenti, G.Toscani,
The theory of nonlinear Botzmann equation for Maxwell
molecules in Fourier representation Ann.Matem. Pura
Appl. Vol. CLXXI (1996) 181-204
63. E. Gabetta, L. Pareschi, G.
Toscani, Wild's sums and numerical approximation of nonlinear kinetic
equations, Transp.The. & Stat. Phys. 25 (1996)
515-530
64. E.Gabetta, G.Toscani,
B.Wennberg The Tanaka functional and exponential convergence for non cut-off molecules, Transp.The. & Stat. Phys. 25 (1996) 543-554
65. A.V. Bobylev, G.Toscani,
Two dimensional half-space problems for the Broadwell
discrete velocity model, Continuum Mech.Thermodyn. 8,
(1996) 257-274
66. G.Toscani, Kinetic approach to the asymptotic behaviour of the solution to diffusion equations Rendic. di Matem.Serie VII 16
(1996) 329-346
67. G.Toscani, On regularity and asymptotic behaviour
of a spatially homogeneous Maxwell gas Rendiconti Circolo Mat.Palermo Suppl. 45
(1996) 649-662
68. A. Pulvirenti, G.Toscani,
Fast diffusion as a limit of a two-velocity kinetic model Rendiconti
Circolo Mat. Palermo Suppl. 45 (1996) 521-528
69. E. Gabetta, L. Pareschi, G.
Toscani, Relaxation schemes for nonlinear kinetic equations, SIAM J. Numer.Anal. 34 (1997) 2168--2194
70. P.L.Lions, G.Toscani,
Diffusive limits for finite velocity Boltzmann kinetic models, Revista Mat. Iberoamer. 13 (1997)
473--513
71. V.Comincioli, G.Naldi,
G.Toscani, The diffusive
limit of two velocity models: the porous medium equation, Transp.The.
& Stat. Phys. 26 (1997) 49-63
72. G.
Toscani, Sur l'inégalité logarithmique
de Sobolev CRAS 324, S'erie I (1997) 689-694
73. S. Jin, L. Pareschi, G. Toscani, Diffusive relaxation
schemes for multiscale
discrete-velocity kinetic equations, SIAM J. Numer. Anal. 35 2405-2439 (1998)
74. A. Pulvirenti, G. Toscani, On the grazing collision
limit for the spatially homogeneous Boltzmann equation Rendiconti
Circolo Mat.Palermo Suppl.
57 (1998) 405-412
75. G. Toscani, The grazing collisions asymptotics
of the non cut-off Kac
equation, M2AN Math.Model. Numer.
Anal., 32 (1998) pp 763-772
76. J.A. Carrillo, G. Toscani, Exponential convergence
toward equilibrium for homogeneous Fokker-Planck-type equations, Math.Methods Appl. Sci., 21 (1998) 1269-1286
77. E.A. Carlen, E. Gabetta, G. Toscani, Propagation of
smoothness and the rate of exponential convergence to equilibrium for a
spatially homogeneous Maxwellian gas, Commun.Math.
Phys. 199, 521-546 (1999).
78. G. Toscani, C. Villani Probability metrics and
uniqueness of the solution to the Boltzmann equation for a Maxwell gas, J. Statist.Phys., 94 619-637 (1999)
79. G. Naldi, L. Pareschi, G.
Toscani, Hyperbolic relaxation approximation to nonlinear parabolic problems,
on International Series of Numerical Mathematics, 130 Birkhäuser
Verlag, Basel (1999) 747-756
80. G. Toscani, C. Villani, Sharp entropy dissipation
bounds and explicit rate of trend to equilibrium for the spatially homogeneous
Boltzmann equation, Commun.Math. Phys. 203, (1999)
667-706
81. G. Toscani, Entropy production and the rate of
convergence to equilibrium for the Fokker-Planck equation, Quarterly of Appl.Math., Vol. LVII (1999), 521-541
82. G. Toscani, Remarks on entropy and equilibrium states,
Appl.Math. Letters, 12 (1999) 19-25
83. S. Jin, L. Pareschi, G.
Toscani, Uniformly accurate diffusive relaxation
schemes for multiscale transport equations, SIAM J. Numerical Analysis 38, 13,
(2000) pp. 913-936.
84. A. Arnold, P. Markowich, G. Toscani, On large time asymptotics for drift-diffusion-Poisson systems, Transport
Theory Statist.Phys. 29 (2000), no. 3-5, 571--581.
85. L. Pareschi, G. Russo, G.
Toscani, Fast spectral methods for the Fokker-Planck-Landau equation, J. Comput.Phys. 165 (2000), 216--236.
86. G. Toscani, C. Villani, On the trend to equilibrium
for some dissipative systems with slowing increasing a priori bounds, J. Statist.Phys., 98 (2000) 1279--1309
87. L.
Pareschi, G.Russo, G.
Toscani, Méthode spéctrale
rapide pour l'équation de Fokker-Planck-Landau, CRAS
330, Série I, (2000) 517--522
88. J. A. Carrillo, G. Toscani, Asymptotic L1-decay of the
porous medium equation to self-similarity , Indiana Univ.Math. J., 46 (2000), 113--142
89. A. Arnold, P. Markowich, G. Toscani, A. Unterreiter, On generalized Csiszar--Kullback
inequalities, Monatschefte für Mathematik,
131, (2000) 235--253,
90. G. Toscani, One-dimensional kinetic models with dissipative
collisions, M2AN Math.Model. Numer.
Anal., 34 (2000), 1277-1292
91. V. Comincioli, G. Naldi, L. Pareschi, G. Toscani, Numerical methods for multiscale
hyperbolic systems and nonlinear parabolic equations, Ann.Univ.
Ferrara, Sez. 7, Vol. XLV Suppl., (2000) 255--266
92. G. Naldi, L. Pareschi, G.
Toscani, Convergence of kinetic approximation to nonlinear parabolic problems,
in Godunov Methods (Oxford 1999), E.F. Toro (Editor), 655--662 Kluwer/ Plenum
Publishers, New York (2001)
93. A. Jüngel, P.A. Markowich,
G. Toscani, Decay rates for solutions of degenerate parabolic systems, Electron.J. Diff. Eqns., Conf. 06, (2001), pp. 189-202.
94. A. Arnold, P. Markowich, G. Toscani, A. Unterreiter, On convex Sobolev inequalities and the rate of
convergence to equilibrium for Fokker-Planck type equations, Commun.Partial Diff. Equa. 26
(2001), 43-100
95. J.A. Carrillo, A. Jüngel,
P.A. Markowich, G. Toscani, A. Unterreiter, Entropy
dissipation methods for degenerate parabolic equations and systems and
generalized Sobolev inequalities, Monatschefte für Mathematik, 133 (2001), 1-82
96. J.L. Lopez, J. Soler, G. Toscani, Time rescaling and
asymptotic behavior of some fourth order degenerate diffusion equations, Comput.Math. Appl., 43 (2002) 721-736
97. G. Naldi, L. Pareschi, G.
Toscani, Relaxation schemes for partial differential equations and applications
to degenerate diffusion problems, Surv.Math. Ind. 10,
(2002) 315--343
98. V. Comincioli, G. Naldi, T. Scapolla, G. Toscani, Multiscale hyperbolic equations:
numerical approximation in the diffusive regime, in Recent Trends in Numerical
Analysis, L. Brugnano& D. Trigiante
Eds. Nova Science Publishers, (2001)
99. J.A. Carrillo, G. Toscani, Long-Time asymptotics for strong solutions of the thin film equation,
Commun.Math. Phys., 225 (2002) 551-571
100. J.A. Carrillo, C. Lederman, P.A. Markowich and G.
Toscani, Poincare Inequalities for Linearizations of
Very Fast Diffusion Equations, Nonlinearity 15, (2002) 565-580
101. T. Goudon, S. Junca, G. Toscani, Fourier-based distances and Berry-Esseen like inequalities for smooth densities, Monatschefte für Mathematik, 135
(2002) 115-136
102. L. Gosse, G. Toscani, An
asymptotic preserving well-balanced scheme for the hyperbolic heat equation,
CRAS Série I, 334 (2002) 1-6
103. L. Gosse, G. Toscani, Space localization and
well-balanced scheme for discrete kinetic models in diffusive regimes, SIAM J. Numer.Anal. 41, (2) (2003) 641-658
104. G. Naldi, L. Pareschi, G.
Toscani, Spectral methods for one-dimensional kinetic models of granular flows
and numerical quasi-elastic limit, M2AN Math.Model. Numer. Anal., 37, (2003) 73-90
105. A. Jüngel, G. Toscani, Decay
rates of solutions to a nonlinear fourth--order parabolic equation, Z. Angew.Math. Phys. 54, (2003) 377-386
106. F. Frommlet, J.L. López, J.
Soler, G. Toscani, Nonlinear rescaling, dispersion lemmas and conservation laws
for some linear kinetic and quantum-kinetic problems.Comm.
Appl. Nonlinear Anal. 10 (2003), 1--20.
107. G. Toscani, Entropy methods for the asymptotic behaviour of fourth-order nonlinear diffusion equations.
"WASCOM 2001"-11th Conference on Waves and Stability in Continuous
Media (Porto Ercole, june 3-9, 2001
), World Sci.Publishing, River Edge, NJ,
(2002) 569--578.
108. L. Pareschi, G. Toscani, C.
Villani, Spectral methods for the non
cut-off Boltzmann equation and numerical grazing collision limit,
Numer.Math., 93 (2003) 527-548
109. A.V. Bobylev, C. Cercignani,
G. Toscani, Proof of an asymptotic property of self-similar solutions of the
Boltzmann equation for granular materials, J. Statist.Phys.,
111 (2003) 403-417
110. M.P. Gualdani, A. Jüngel, G. Toscani, Exponential decay in time of solutions
of the viscous quantum hydrodynamic equations, Appl.Math.
Letters, 16 (2003) 1273-1278
111. L. Gosse, G. Toscani, Asymptotic preserving and
well-balanced schemes for radiative transfer and the Rosseland approximation, Numer.Math. 98 ( 2) (2004) 223 -
250
112. M. Bisi, G. Spiga, G. Toscani, Hydrodynamics from
grad's equations for weakly inelastic granular flows, Physics of Fluids 16 (12)
(2004) 4235-4247
113. Hailiang Li, G. Toscani, Long-time asymptotics
of kinetic models of granular flows, Arch.Ration.
Mech. Anal., 172 (3) (2004) 407-428
114. B. Lods, G. Toscani, The dissipative linear Boltzmann
equation for hard spheres, J. Statist.Phys., 117
(3-4) (2004) 635-664
115. A. Pulvirenti, G. Toscani, Probabilistic treatment of
some dissipative kinetic models, in "WASCOM 2003"-12th Conference on
Waves and Stability in Continuous Media, World Sci. Publishing, River Edge, NJ,
( 2004) 407--420
116. G. Toscani et al. Entropy and equilibria of many
particle systems: an essay on recent research.Monatschefte
für Mathematik, 142 (1-2) (2004) 35-43
117. L. Pareschi, G. Toscani,
Modelling and numerical methods for granular gases, in "Modeling and
Computational Methods for Kinetic Equations", P. Degond,
L. Pareschi and G. Russo Eds., Birkhauser,
Boston (2004) 259-285
118. M. Bisi, G. Toscani, Self-similar solutions of a nonlinear
friction equation in higher dimensions, Ann.Univ.
Ferrara - Sez 7 - Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Vol. L, (2004)
91-110.
119. J.A. Carrillo, M.P. Gualdani,
G. Toscani, Finite speed of propagation in porous media by mass transportation
methods, CRAS Série I, 338 (10) (2004) 815-818
120. A. Pulvirenti, G. Toscani, Asymptotic properties of
the inelastic Kac model, J. Statist.Phys., 114 (2004)
1453-1480
121. J.A. Carrillo, G. Toscani, Wasserstein metric and
large-time asymptotics of nonlinear diffusion
equations, in New trends in mathematical physics,
World Sci.Publ., Hackensack, NJ, (2004) 234–244.
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