COMPLETE LIST OF PUBLICATIONS
RECENT PAPERS
( updated January 12, 2024 )
- P. Colli, G. Gilardi, A. Signori & J. Sprekels,
Curvature effects in pattern formation: well-posedness and optimal control
of a sixth-order Cahn–Hilliard equation,
preprint arXiv:2401.05189 [math.AP] (2024) 1-45
- P. Colli, P. Knopf, G. Schimperna & A. Signori,
Two-phase flows through porous media described by a Cahn–Hilliard–Brinkman model
with dynamic boundary conditions,
preprint arXiv:2312.15274 [math.AP] (2023) 1-42
- P. Colli, G. Gilardi & G. Marinoschi,
Global solution and optimal control of an epidemic
propagation with a heterogeneous diffusion,
Appl. Math. Optim. 89 (2024), no. 1, 28 pp.
doi:10.1007/s00245-023-10094-2
preprint arXiv:2308.08251 [math.OC] (2023)
- A. Agosti, P. Colli & M. Frémond,
Large deformations in terms of stretch and rotation and global solution to the quasi-stationary problem,
preprint arXiv:2307.02992 [math.AP] (2023) 1-31
- P. Colli, G. Gilardi, G. Marinoschi & E. Rocca,
Optimal control of a reaction-diffusion model related to the spread of COVID-19,
Anal. Appl. (Singap.) 22 (2024), 111-136
doi:110.1142/S0219530523500197
preprint arXiv:2304.11114 [math.OC] (2023)
- P. Colli, G. Gilardi, A. Signori & J. Sprekels,
Optimal temperature distribution for a nonisothermal Cahn–Hilliard system in two dimensions
with source term and double obstacle potential,
Ann. Acad. Rom. Sci. Ser. Math. Appl. 15 (2023), 175-204
doi:10.56082/annalsarscimath.2023.1-2.175
preprint arXiv:2303.13266 [math.OC] (2023)
- P. Colli, G. Gilardi, A. Signori & J. Sprekels,
Optimal temperature distribution for a nonisothermal Cahn–Hilliard system with source term,
Appl. Math. Optim. 88 (2023), Paper No. 68, 31 pp.
doi:10.1007/s00245-023-10039-9
preprint arXiv:2303.00488 [math.OC] (2023)
- A. Agosti, P. Colli, H. Garcke & E. Rocca,
A Cahn–Hilliard phase field model coupled to an Allen–Cahn model of viscoelasticity at large strains,
Nonlinearity 36 (2023), 6589-6638
doi:10.1088/1361-6544/ad0211
preprint arXiv:2301.08341 [math.AP] (2023)
- P. Colli, T. Fukao & L. Scarpa,
A Cahn–Hilliard system with forward-backward dynamic boundary condition and non-smooth potentials,
J. Evol. Equ. 22 (2022), Paper No. 89, 31 pp.
doi:10.1007/s00028-022-00847-x
preprint arXiv:2208.00664 [math.AP] (2022)
- P. Colli, G. Gilardi, A. Signori & J. Sprekels,
On a Cahn–Hilliard system with source term and thermal memory,
Nonlinear Anal. 240 (2024), Paper No. 113461, 16 pp.
doi:10.1016/j.na.2023.113461
preprint arXiv:2207.08491 [math.AP] (2022)
- P. Colli, G. Gilardi, A. Signori & J. Sprekels,
Optimal control of a nonconserved phase field model of Caginalp type
with thermal memory and double obstacle potential,
Discrete Contin. Dyn. Syst. Ser. S 16 (2023), 2305-2325
doi:10.3934/dcdss.2022210
preprint arXiv:2207.00375 [math.OC] (2022)
- P. Colli, G. Gilardi, A. Signori & J. Sprekels,
Cahn–Hilliard–Brinkman model for tumor growth with possibly singular potentials,
Nonlinearity 36 (2023), 4470-4500
doi:10.1088/1361-6544/ace2a7
preprint arXiv:2204.13526 [math.AP] (2022)
- A. Agosti, P. Colli, H. Garcke & E. Rocca,
A Cahn–Hilliard model coupled to viscoelasticity with large deformations,
Commun. Math. Sci. 21 (2023), 2083-2130
doi:10.4310/cms.2023.v21.n8.a2
preprint arXiv:2204.04951 [math.AP] (2022)
- F. Auricchio, P. Colli, G. Gilardi, A. Reali & E. Rocca,
Well-posedness for a diffusion-reaction compartmental model simulating the spread of COVID-19,
Math. Methods Appl. Sci. 46 (2023), 12529-12548
doi:10.1002/mma.9196
preprint arXiv:2203.10869 [math.AP] (2022)
- P. Colli, G. Gilardi, E. Rocca & J. Sprekels,
Well-posedness and optimal control for a Cahn–Hilliard–Oono system with control in the mass term,
Discrete Contin. Dyn. Syst. Ser. S 15 (2022), 2135-2172
doi:10.3934/dcdss.2022001
preprint arXiv:2108.03165 [math.AP] (2021)
- P. Colli, A. Signori & J. Sprekels,
Analysis and optimal control theory for a phase field model of Caginalp type with thermal memory,
Commun. Optim. Theory 2022 (2022), Article ID 4, 31 pp.
doi:10.23952/cot.2022.4
preprint arXiv:2107.09565 [math.OC] (2021)
- P. Colli, T. Fukao & L. Scarpa,
The Cahn–Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity,
SIAM J. Math. Anal. 54 (2022), 3292-3315
doi:10.1137/21M142441X
preprint arXiv:2106.01010 [math.AP] (2021)
- P. Colli, A. Signori & J. Sprekels,
Optimal control problems with sparsity for phase field tumor growth models involving variational inequalities,
J. Optim. Theory Appl. 194 (2022), 25-58
doi:10.1007/s10957-022-02000-7
preprint arXiv:2104.09814 [math.OC] (2021)
- P. Colli, G. Gilardi & J. Sprekels,
Well-posedness for a class of phase-field systems modeling prostate cancer growth
with fractional operators and general nonlinearities,
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 33 (2022), 193-228
doi:10.4171/rlm/969
preprint arXiv:2104.00444 [math.AP] (2021)
- P. Colli, A. Signori & J. Sprekels,
Correction to: Optimal control of a phase field system modelling tumor growth
with chemotaxis and singular potentials,
Appl. Math. Optim. 84 (2021), 3569-3570
doi:10.1007/s00245-021-09771-x
- G. Gilioli, P. Colli, M. Colturato, P. Gervasio & G. Sperandio,
A nonlinear model for stage-structured population dynamics with nonlocal density-dependent regulation:
an application to the fall armyworm moth,
Math. Biosci. 335 (2021), 108573, 13 pp.
doi:10.1016/j.mbs.2021.108573
- P. Colli, A. Signori & J. Sprekels,
Second-order analysis of an optimal control problem in a phase field
tumor growth model with singular potentials and chemotaxis,
ESAIM Control Optim. Calc. Var. 27 (2021), Paper No. 73, 46 pp.
doi:10.1051/cocv/2021072
preprint arXiv:2009.07574 [math.OC] (2020)
- P. Colli, H. Gomez, G. Lorenzo, G. Marinoschi, A. Reali & E. Rocca,
Optimal control of cytotoxic and antiangiogenic therapies on prostate cancer growth,
Math. Models Methods Appl. Sci. 31 (2021), 1419-1468
doi:10.1142/S0218202521500299
preprint arXiv:2007.05098 [math.OC] (2020)
- P. Colli, G. Gilardi & J. Sprekels,
An asymptotic analysis for a generalized Cahn–Hilliard system with fractional operators,
J. Evol. Equ. 21 (2021), 2749-2778
doi:10.1007/s00028-021-00706-1
preprint arXiv:2007.04708 [math.AP] (2020)
- P. Colli, G. Gilardi & J. Sprekels,
Optimal control of a phase field system of
Caginalp type with fractional operators,
Pure Appl. Funct. Anal.
7 (2022), 1597-1635
preprint arXiv:2005.11948 [math.AP] (2020)
- P. Colli & T. Fukao,
Vanishing diffusion in a dynamic boundary condition for the
Cahn–Hilliard equation,
NoDEA Nonlinear Differential Equations Appl. 27 (2020), Paper No. 53, 27 pp.
doi:10.1007/s00030-020-00654-8
preprint arXiv:2004.06953 [math.AP] (2020)
- P. Colli, G. Gilardi & G. Marinoschi,
Solvability and sliding mode control for the viscous Cahn–Hilliard
system with a possibly singular potential,
Math. Control Relat. Fields 11 (2021), 905-934
doi:10.3934/mcrf.2020051
preprint arXiv:2004.00982 [math.AP] (2020)
- P. Colli, M.H. Farshbaf-Shaker, K. Shirakawa & N. Yamazaki,
Optimal control for shape memory alloys of the one-dimensional Frémond model,
Numer. Funct. Anal. Optim. 41 (2020), 1421-1471
doi:10.1080/01630563.2020.1774892
- P. Colli & D. Manini,
Sliding mode control for a generalization
of the Caginalp phase-field system,
Appl. Math. Optim. 84 (2021), 1395-1433
doi:10.1007/s00245-020-09682-3
preprint arXiv:1911.01481
[math.AP] (2019)
- P. Colli, G. Gilardi & J. Sprekels,
Asymptotic analysis of a tumor growth model
with fractional operators,
Asymptot. Anal. 120 (2020), 41-72
doi:10.3233/ASY-191578
preprint arXiv:1908.10651
[math.AP] (2019)
- E. Bonetti, P. Colli, L. Scarpa & G. Tomassetti,
Bounded solutions and their asymptotics for a doubly
nonlinear Cahn–Hilliard system,
Calc. Var. Partial Differential Equations 59 (2020), Paper No. 88, 25 pp.
doi:10.1007/s00526-020-1715-9
preprint arXiv:1908.02079
[math.AP] (2019)
- P. Colli, T. Fukao & H. Wu,
On a transmission problem for equation and dynamic boundary condition
of Cahn–Hilliard type with nonsmooth potentials,
Math. Nachr. 293 (2020), 2051-2081
doi:10.1002/mana.201900361
preprint arXiv:1907.13278
[math.AP] (2019)
- P. Colli, H. Gomez, G. Lorenzo, G. Marinoschi, A. Reali & E. Rocca,
Mathematical analysis and simulation study of a phase-field model
of
prostate cancer growth with chemotherapy and antiangiogenic therapy effects,
Math. Models Methods Appl. Sci. 30 (2020), 1253-1295
doi:10.1142/S0218202520500220
preprint arXiv:1907.11618
[math.AP] (2019)
- P. Colli, G. Gilardi & J. Sprekels,
A distributed control problem for a fractional tumor growth model,
Mathematics 7 (2019), 792
doi:10.3390/math7090792
preprint arXiv:1907.10452 [math.OC] (2019)
- P. Colli, A. Signori & J. Sprekels,
Optimal control of a phase field system modelling tumor growth
with chemotaxis and singular potentials,
Appl. Math. Optim. 83 (2021), 2017-2049
doi:10.1007/s00245-019-09618-6
preprint arXiv:1907.03566
[math.AP] (2019)
- P. Colli, G. Gilardi & J. Sprekels,
Well-posedness and regularity for a fractional tumor growth model,
Adv. Math. Sci. Appl. 28 (2019), 343-375
preprint arXiv:1906.10874
[math.AP] (2019)
- P. Colli & A. Signori,
Boundary control problem and optimality conditions for the Cahn–Hilliard
equation with dynamic boundary conditions,
Internat. J. Control 94 (2021), 1852-1869
doi:10.1080/00207179.2019.1680870
preprint arXiv:1905.00203
[math.AP] (2019)
- P. Colli, G. Gilardi & J. Sprekels,
Longtime behavior for a generalized Cahn-Hilliard system with fractional
operators,
Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 98 (2020), suppl. 2, A4, 18 pp.
doi:10.1478/AAPP.98S2A4
preprint arXiv:1904.00931
[math.AP] (2019)
- P. Colli & S. Kurima,
Global existence for a phase separation system
deduced from the entropy balance,
Nonlinear Anal. 190 (2020), 111613, 31 pp.
doi:10.1016/j.na.2019.111613
preprint arXiv:1901.10158
[math.AP] (2019)
- P. Colli, G. Gilardi & J. Sprekels,
Deep quench approximation
and optimal control of general Cahn–Hilliard systems
with fractional operators and double obstacle potentials,
Discrete Contin. Dyn. Syst. Ser. S 14 (2021), 243-271
doi:10.3934/dcdss.2020213
preprint arXiv:1812.01675
[math.AP] (2018)
- P. Colli, G. Gilardi & J. Sprekels,
Nonlocal
phase field models of viscous Cahn–Hilliard type,
in `Topics in Applied Analysis and Optimisation
(Stochastic, Partial Differential Equations and Numerical Analysis)',
M. Hintermüller, J.F. Rodrigues (ed.),
CIM Series in Mathematical Sciences, Springer, Cham, 2019, pp. 71-100
doi:10.1007/978-3-030-33116-0_3
- P. Colli, G. Gilardi & I. Munteanu,
Stabilization of a linearized
Cahn–Hilliard system for phase separation by proportional boundary feedbacks,
Internat. J. Control 94 (2021), 452-460
doi:10.1080/00207179.2019.1597280
preprint arXiv:1811.12662
[math.AP] (2018)
- P. Colli & S. Kurima,
Time discretization of
a nonlinear phase field system in general domains,
Comm. Pure Appl. Anal. 18 (2019), 3161-3179
doi:10.3934/cpaa.2019142
preprint arXiv:1811.10730
[math.AP] (2018)
- P. Colli, G. Gilardi & J. Sprekels,
Optimal distributed control of a
generalized fractional Cahn–Hilliard system,
Appl. Math. Optim. 82 (2020), 551-589
doi:10.1007/s00245-018-9540-7
preprint arXiv:1807.03218
[math.AP] (2018)
- P. Colli & G. Gilardi,
Well-posedness, regularity and asymptotic analyses
for a fractional phase field system,
Asymptot. Anal. 114 (2019), 93-128
doi:10.3233/asy-191524
preprint arXiv:1806.04625
[math.AP] (2018)
- P. Colli, G. Gilardi & J. Sprekels,
Well-posedness and regularity for a
generalized fractional Cahn–Hilliard system,
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), 437-478
doi:10.4171/RLM/855
preprint arXiv:1804.11290 [math.AP] (2018)
- P. Colli, T. Fukao & K.F. Lam,
On a coupled bulk-surface Allen–Cahn system with an affine linear transmission condition
and its approximation by a Robin boundary condition,
Nonlinear Anal. 184 (2019), 116-147
doi:10.1016/j.na.2018.10.018
preprint arXiv:1803.08291
[math.AP] (2018)
- P. Colli & T. Fukao,
Cahn–Hilliard equation on the boundary with bulk condition of Allen–Cahn type,
Adv. Nonlinear Anal. 9 (2020), 16-38
doi:10.1515/anona-2018-0055
preprint arXiv:1803.05314
[math.AP] (2018)
- P. Colli, G. Gilardi & J. Sprekels,
On the longtime behavior of a viscous
Cahn–Hilliard system with convection and dynamic boundary conditions,
J. Elliptic Parabol. Equ. 4 (2018), 327-347
doi:10.1007/s41808-018-0021-6
preprint arXiv:1803.04318
[math.AP] (2018)
- E. Bonetti, P. Colli, L. Scarpa & G. Tomassetti,
A
doubly nonlinear Cahn–Hilliard system with nonlinear viscosity,
Comm. Pure Appl. Anal. 17 (2018), 1001-1022
doi:10.3934/cpaa.2018049
preprint arXiv:1710.06698
[math.AP] (2017)
- P. Colli, G. Gilardi & J. Sprekels,
Optimal velocity control of
a convective Cahn–Hilliard system with double obstacles
and dynamic boundary conditions: a `deep quench' approach,
J. Convex Anal. 26 (2019), 485-514
JCA/JCA26/JCA262/jca26024
preprint arXiv:1709.03892
[math.AP] (2017)
- P. Colli, G. Gilardi & J. Sprekels,
Optimal velocity
control of a viscous Cahn–Hilliard system with convection
and dynamic boundary conditions,
SIAM J. Control Optim. 56 (2018), 1665-1691
doi:10.1137/17M1146786
preprint arXiv:1709.02335
[math.AP] (2017)
- P. Colli, G. Gilardi, G. Marinoschi & E. Rocca,
Optimal
control for a conserved phase field system with a possibly singular potential,
Evol. Equ. Control Theory 7 (2018), 95-116
doi:10.3934/eect.2018006
preprint arXiv:1709.02269
[math.AP] (2017)
- P. Colli & M. Colturato,
Global existence for a singular
phase field system related to a sliding mode control problem,
Nonlinear Anal. Real World Appl. 41 (2018), 128-151
doi:10.1016/j.nonrwa.2017.10.011
preprint arXiv:1706.08108
[math.AP] (2017)
- P. Colli, G. Gilardi, G. Marinoschi & E. Rocca,
Sliding
mode control for a phase field system related to tumor growth,
Appl. Math. Optim. 79 (2019), 647-670
doi:10.1007/s00245-017-9451-z
preprint arXiv:1706.03564
[math.AP] (2017)
- P. Colli, G. Gilardi & J. Sprekels,
On a Cahn–Hilliard
system with convection and dynamic boundary conditions,
Ann. Mat. Pura Appl. (4) 197 (2018), 1445-1475
doi:10.1007%2Fs10231-018-0732-1
preprint arXiv:1704.05337
[math.AP] (2017)
- P. Colli & J. Sprekels,
Optimal boundary control
of a nonstandard Cahn–Hilliard system
with dynamic boundary condition and double obstacle inclusions,
in `Solvability, Regularity, Optimal Control of Boundary Value Problems for PDEs',
P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels (ed.),
Springer INdAM Series 22, Springer, Cham, 2017, pp. 151-182
doi:10.1007/978-3-319-64489-9_7
preprint arXiv:1702.01907
[math.AP] (2017)
- P. Colli, G. Gilardi & J. Sprekels,
Limiting problems
for a nonstandard viscous Cahn–Hilliard system
with dynamic boundary conditions,
in `Trends on Applications of Mathematics to Mechanics',
E. Rocca, U. Stefanelli, L. Truskinovski, A. Visintin (ed.),
Springer INdAM Series 27, Springer, Cham, 2018, pp. 217-242
doi:10.1007/978-3-319-75940-1_11
preprint arXiv:1702.00762
[math.AP] (2017)
- P. Colli, G. Gilardi & J. Sprekels,
Recent
results on the Cahn–Hilliard equation with
dynamic boundary conditions,
Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 10 (2017), 5-21
doi:10.14529/mmp170101
- P. Colli, G. Gilardi, R. Nakayashiki & K. Shirakawa,
A
class of quasi-linear Allen–Cahn type equations
with dynamic boundary conditions,
Nonlinear Anal. 158 (2017), 32-59
doi:10.1016/j.na.2017.03.020
preprint arXiv:1610.08687
[math.AP] (2016)
- P. Colli, G. Gilardi & J. Sprekels,
Optimal
boundary control of a nonstandard viscous Cahn–Hilliard
system with dynamic boundary condition,
Nonlinear Anal. 170 (2018), 171-196
doi:10.1016/j.na.2018.01.003
preprint arXiv:1609.07046
[math.AP] (2016)
- P. Colli, G. Gilardi & J. Sprekels,
Global
existence for a nonstandard viscous Cahn–Hilliard system
with dynamic boundary condition,
SIAM J. Math. Anal. 49 (2017), 1732-1760
doi:10.1137/16M1087539
preprint arXiv:1608.00854
[math.AP] (2016)
- P. Colli, G. Gilardi & J. Sprekels,
Distributed optimal control of a nonstandard nonlocal
phase field system with double obstacle potential,
Evol. Equ. Control Theory 6 (2017), 35-58
doi:10.3934/eect.2017003
preprint arXiv:1607.01991
[math.AP] (2016)
- V. Barbu, P. Colli, G. Gilardi & G. Marinoschi,
Feedback stabilization of the Cahn–Hilliard type system for phase separation,
J. Differential Equations 262 (2017), 2286-2334
doi:10.1016/j.jde.2016.10.047
preprint arXiv:1606.09230
[math.AP] (2016)
- P. Colli, G. Gilardi & J. Sprekels,
Distributed optimal control of a nonstandard nonlocal phase field system,
AIMS Mathematics 1 (2016), 225-260
doi:10.3934/Math.2016.3.225
preprint arXiv:1605.07801
[math.AP] (2016)
- P. Colli & L. Scarpa,
From the viscous
Cahn–Hilliard equation to a regularized
forward-backward parabolic equation,
Asymptot. Anal. 99 (2016), 183-205
doi:10.3233/ASY-161380
preprint arXiv:1605.03857
[math.AP] (2016)
- P. Colli, G. Gilardi & J. Sprekels,
Constrained evolution for a quasilinear parabolic equation,
J. Optim. Theory Appl. 170 (2016), 183-205
doi:10.1007/s10957-016-0970-6
preprint arXiv:1602.07237
[math.AP] (2016)
- P. Colli, G. Gilardi, E. Rocca & J. Sprekels,
Optimal distributed control of a diffuse
interface model of tumor growth,
Nonlinearity 30 (2017), 2518-2546
doi:10.1088/1361-6544/aa6e5f
preprint arXiv:1601.04567
[math.AP] (2016)
- P. Colli & T. Fukao,
Nonlinear diffusion equations as asymptotic
limits of Cahn–Hilliard systems,
J. Differential Equations 260 (2016), 6930-6959
doi:10.1016/j.jde.2016.01.032
preprint arXiv:1511.08853
[math.AP] (2015)
- P. Colli, G. Gilardi & J. Sprekels,
On an application of Tikhonov's fixed point theorem
to a nonlocal Cahn–Hilliard type system modeling phase separation,
J. Differential Equations 260 (2016), 7940-7964
doi:10.1016/j.jde.2016.02.011
preprint arXiv:1511.04361
[math.AP] (2015)
- E. Bonetti, P. Colli & G. Tomassetti,
A non-smooth regularization of a forward-backward parabolic equation,
Math. Models Methods Appl. Sci. 27 (2017), 641-661
doi:10.1142/S0218202517500129
preprint arXiv:1508.03225
[math.AP] (2015)
- V. Barbu, P. Colli, G. Gilardi, G. Marinoschi & E. Rocca,
Sliding mode control for a nonlinear phase-field system,
SIAM J. Control Optim. 55 (2017), 2108-2133
doi:10.1137/15M102424X
preprint arXiv:1506.01665
[math.AP] (2015)
- P. Colli & L. Scarpa,
Existence of solutions for a model of microwave heating,
Discrete Contin. Dyn. Syst. 36 (2016), 3011-3034
doi:10.3934/dcds.2016.36.3011
preprint arXiv:1505.03280
[math.AP] (2015)
- P. Colli, G. Gilardi & J. Sprekels,
A boundary control problem for the pure Cahn–Hilliard equation
with dynamic boundary conditions,
Adv. Nonlinear Anal. 4 (2015), 311-325
doi:10.1515/anona-2015-0035
preprint arXiv:1503.03213
[math.AP] (2015)
- P. Colli, G. Gilardi, E. Rocca & J. Sprekels,
Asymptotic analyses and error estimates for a Cahn–Hilliard
type phase field system modelling tumor growth,
Discrete Contin. Dyn. Syst. Ser. S 10 (2017), 37-54
doi:10.3934/dcdss.2017002
preprint arXiv:1503.00927
[math.AP] (2015)
- P. Colli & T. Fukao,
Equation and dynamic boundary condition of Cahn–Hilliard type
with singular potentials,
Nonlinear Anal. 127 (2015), 413-433
doi:10.1016/j.na.2015.07.011
preprint arXiv:1502.05159
[math.AP] (2015)
- P. Colli, G. Gilardi, E. Rocca & J. Sprekels,
Vanishing viscosities and error estimate for a Cahn–Hilliard
type phase field system related to tumor growth,
Nonlinear Anal. Real World Appl. 26 (2015), 93-108
doi:10.1016/j.nonrwa.2015.05.002
preprint arXiv:1501.07057 [math.AP] (2015)
- P. Colli, G. Gilardi & G. Marinoschi,
A boundary control problem for a possibly singular phase field
system with dynamic boundary conditions,
J. Math. Anal. Appl. 434 (2016), 432-463
doi:10.1016/j.jmaa.2015.09.011
preprint arXiv:1501.04517
[math.AP] (2015)
- P. Colli & T. Fukao,
Cahn–Hilliard equation with dynamic boundary conditions
and mass constraint on the boundary,
J. Math. Anal. Appl. 429 (2015), 1190-1213
doi:10.1016/j.jmaa.2015.04.057
preprint arXiv:1412.1932
[math.AP] (2014)
- P. Colli, M.H. Farshbaf-Shaker, G. Gilardi & J. Sprekels,
Second-order analysis of a boundary control problem for the viscous
Cahn–Hilliard equation with dynamic boundary condition,
Ann.
Acad. Rom. Sci. Ser. Math. Appl. 7 (2015), 41-66
preprint arXiv:1410.8443
[math.AP] (2014)
- P. Colli, G. Gilardi, G. Marinoschi & E. Rocca,
Optimal control for a phase field system with a
possibly singular potential,
Math. Control Relat. Fields 6 (2016), 95-112
doi:10.3934/mcrf.2016.6.95
preprint arXiv:1410.6718
[math.AP] (2014)
- P. Colli, M.H. Farshbaf-Shaker, G. Gilardi & J. Sprekels,
Optimal boundary control of a viscous Cahn–Hilliard system
with
dynamic boundary condition and double obstacle potentials,
SIAM J. Control Optim. 53 (2015), 2696-2721
doi:10.1137/140984749
preprint arXiv:1408.6146
[math.AP] (2014)
- P. Colli, G. Gilardi & J. Sprekels,
A boundary control problem for the viscous Cahn–Hilliard equation
with dynamic boundary conditions,
Appl. Math. Optim. 73 (2016), 195-225
doi:10.1007/s00245-015-9299-z
preprint arXiv:1407.3916
[math.AP] (2014)
- P. Colli & T. Fukao,
The Allen–Cahn equation with dynamic
boundary conditions and mass constraints,
Math. Methods Appl. Sci. 38 (2015), 3950-3967
doi:10.1002/mma.3329
preprint arXiv:1405.0116
[math.AP] (2014)
- P. Colli, G. Marinoschi & E. Rocca,
Sharp interface control in a Penrose-Fife model,
ESAIM Control Optim. Calc. Var. 22 (2016), 473-499
doi:10.1051/cocv/2015014
preprint arXiv:1403.4446
[math.AP] (2014)
- P. Colli, G. Gilardi & J. Sprekels,
On the Cahn–Hilliard equation with dynamic boundary conditions
and a dominating boundary potential,
J. Math. Anal. Appl. 419 (2014), 972-994
doi:10.1016/j.jmaa.2014.05.008
preprint arXiv:1403.1663
[math.AP] (2014)
- P. Colli, G. Gilardi & D. Hilhorst,
On a Cahn-Hilliard type phase field system
related to tumor growth,
Discrete Contin. Dyn. Syst. 35 (2015), 2423-2442
doi:10.3934/dcds.2015.35.2423
preprint arXiv:1401.5943
[math.AP] (2014)
- E. Bonetti, P. Colli & M. Frémond,
The 3D motion of a solid with large deformations,
C. R. Math. Acad. Sci. Paris 352
(2014), 183-187
doi:10.1016/j.crma.2014.01.007
- P. Colli, M.H. Farshbaf-Shaker & J. Sprekels,
A deep quench approach to the optimal control of an Allen–Cahn equation
with dynamic boundary conditions and double obstacles,
Appl. Math. Optim. 71 (2015), 1-24
doi:10.1007/s00245-014-9250-8
preprint arXiv:1308.5617
[math.AP] (2013) (with a slightly different title)
- E. Bonetti, P. Colli, M. Fabrizio & G. Gilardi,
Existence of solutions for a mathematical model
related to solid-solid phase transitions in shape memory alloys,
Arch. Ration. Mech. Anal. 219 (2016), 203-254
doi:10.1007/s00205-015-0896-4
preprint arXiv:1307.1572
[math.AP] (2013)
- E. Bonetti, P. Colli & M. Frémond,
2D motion with large deformations,
Boll. Unione Mat. Ital. 7 (2014), 19-44
doi:10.1007/s40574-014-0002-0
preprint (2013)
- P. Colli, G. Gilardi, P. Krejčí, P. Podio-Guidugli & J. Sprekels,
Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system,
ESAIM Math. Model. Numer. Anal. 48 (2014), 1061-1087
doi:10.1051/m2an/2014005
preprint arXiv:1304.4503
[math.AP] (2013)
- P. Colli, G. Gilardi & J. Sprekels,
Regularity of the solution to a nonstandard system of phase field equations,
Rend. Cl. Sci. Mat. Nat. 147 (2013), 47-63
doi:10.4081/scie.2013.180
preprint arXiv:1303.3107
[math.AP] (2013)
- P. Colli, G. Gilardi, P. Krejčí & J. Sprekels,
A continuous dependence result for a nonstandard system of phase field equations,
Math. Methods Appl. Sci. 37 (2014), 1318-1324
doi:10.1002/mma.2892
preprint arXiv:1303.3104
[math.AP] (2013)
- E. Bonetti, P. Colli & G. Gilardi,
Singular limit of an integrodifferential system related to the entropy balance,
Discrete Contin. Dyn. Syst. Ser. B 19 (2014), 1935-1953
doi:10.3934/dcdsb.2014.19.1935
preprint arXiv:1301.2806 [math.AP] (2013)
- P. Colli, G. Gilardi, P. Krejčí & J. Sprekels,
A vanishing diffusion limit in a nonstandard system of phase field equations,
Evol. Equ. Control Theory 3 (2014), 257-275
doi:10.3934/eect.2014.3.257
preprint arXiv:1212.4054
[math.AP] (2012)
- P. Colli & J. Sprekels,
Optimal control of an Allen–Cahn equation with singular potentials and dynamic
boundary condition,
SIAM J. Control Optim. 53 (2015), 213-234
doi:10.1137/120902422
preprint arXiv:1212.2359
[math.AP] (2012)
- E. Bonetti, P. Colli & M. Frémond,
The motion of a solid with large deformations,
C. R. Math. Acad. Sci. Paris 351
(2013), 579-583
doi:10.1016/j.crma.2013.06.012
- P. Colli, G. Gilardi, P. Podio-Guidugli & J. Sprekels,
Continuous dependence for a nonstandard Cahn-Hilliard system
with nonlinear atom mobility,
Rend. Semin. Mat. Univ. Politec. Torino 70 (2012), 27-52
WIAS Preprint No. 1742 (2012)
- L. Calatroni & P. Colli,
Global solution to the Allen–Cahn equation with singular potentials
and dynamic boundary conditions,
Nonlinear Anal. 79 (2013), 12-27
doi:10.1016/j.na.2012.11.010
preprint arXiv:1206.6738
[math.AP]
- G. Canevari & P. Colli,
Convergence properties for a generalization of the Caginalp phase field system,
Asymptot. Anal. 82 (2013), 139-162
doi:10.3233/ASY-2012-1142
preprint arXiv:1205.6093
[math.AP]
- P. Colli, G. Gilardi, P. Podio-Guidugli & J. Sprekels,
Global existence and uniqueness for a singular/degenerate
Cahn–Hilliard system with viscosity,
J. Differential Equations 254 (2013), 4217-4244
doi:10.1016/j.jde.2013.02.014
preprint arXiv:1205.4979
[math.AP]
- P. Colli & Ph. Laurençot,
A phase-field approximation of the Willmore flow with volume and area constraints,
SIAM J. Math. Anal. 44 (2012), 3734-3754
doi:10.1137/120874126
preprint arXiv:1204.4274
[math.AP]
- P. Colli, G. Gilardi, P. Podio-Guidugli & J. Sprekels,
Global existence for a strongly coupled Cahn-Hilliard system with viscosity,
Boll. Unione Mat. Ital. (9) 5 (2012), 495-513
preprint arXiv:1202.5210
[math.AP]
- P. Colli, G. Gilardi & J. Sprekels,
Analysis and optimal boundary control of a nonstandard system of phase field equations,
Milan J. Math. 80 (2012), 119-149
doi:10.1007/s00032-012-0181-z
preprint arXiv:1201.5541
[math.AP]
- P. Colli, G. Gilardi, P. Podio-Guidugli & J. Sprekels,
An asymptotic analysis for a nonstandard Cahn-Hilliard system with viscosity,
Discrete Contin. Dyn. Syst. Ser. S 6 (2013), 353-368
doi:10.3934/dcdss.2013.6.353
preprint arXiv:1109.3303
[math.AP]
- E. Bonetti, P. Colli & Ph. Laurençot,
Global existence for a hydrogen storage model with full energy balance,
Nonlinear Anal. 75 (2012), 3558-3573
doi:10.1016/j.na.2012.01.015
preprint arXiv:1108.1332
[math.AP]
- G. Canevari & P. Colli,
Solvability and asymptotic analysis of a generalization of the Caginalp phase field system,
Commun. Pure Appl. Anal. 11 (2012), 1959-1982
doi:10.3934/cpaa.2012.11.1959
preprint arXiv:1107.3950 [math.AP]
- P. Colli, G. Gilardi, P. Podio-Guidugli & J. Sprekels,
Distributed optimal control of a nonstandard system of phase field equations,
Contin. Mech. Thermodyn. 24 (2012), 437-459
doi:10.1007/s00161-011-0215-8
preprint arXiv:1106.3668
[math.AP]
- P. Colli, G. Gilardi, P. Podio-Guidugli & J. Sprekels,
Well-posedness and long-time behavior for a nonstandard viscous Cahn–Hilliard system,
SIAM J. Appl. Math. 71 (2011), 1849-1870
doi:10.1137/110828526
preprint arXiv:1103.4585
[math.AP]
- P. Colli, S. Frigeri & M. Grasselli,
Global existence of weak solutions to a nonlocal Cahn–Hilliard–Navier–Stokes system,
J. Math. Anal. Appl. 386 (2012), 428-444
doi:10.1016/j.jmaa.2011.08.008
preprint arXiv:1101.3906 [math.AP]
- P. Colli, P. Krejčí, E. Rocca & J. Sprekels,
A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity,
J. Differential Equations 251 (2011), 1354-1387
doi:10.1016/j.jde.2011.02.010
preprint
arXiv:1011.4314 [math.AP]
- P. Colli, G. Gilardi, P. Podio-Guidugli & J. Sprekels,
A temperature-dependent phase segregation problem of the Allen-Cahn type,
Adv. Math. Sci. Appl. 20 (2010), 219-234
preprint
arXiv:1005.0911 [math.AP]
- P. Colli & Ph. Laurençot,
A phase-field approximation of the Willmore flow with volume constraint,
Interfaces Free Bound. 13 (2011), 341-351
doi:10.4171/IFB/261
preprint
arXiv:1004.0341 [math.AP]
- P. Colli, G. Gilardi, P. Podio-Guidugli & J. Sprekels,
Existence and uniqueness of a global-in-time solution
to a phase segregation problem of the Allen–Cahn type,
Math. Models Methods Appl. Sci.
20 (2010), 519-541
doi:10.1142/S0218202510004325
preprint
arXiv:0902.4741 [math.AP] (with a slightly different title)
- E. Bonetti, P. Colli, M. Fabrizio & G. Gilardi,
Existence and boundedness of solutions for a
singular phase field system,
J. Differential Equations 246 (2009), 3260-3295
doi:10.1016/j.jde.2009.02.007
preprint arXiv:0804.1628 [math.AP]
- P. Colli, D. Hilhorst, F. Issard-Roch & G. Schimperna,
Long time convergence for a class of variational
phase field models,
Discrete Contin. Dyn. Syst.
25 (2009), 63-81
doi:10.3934/dcds.2009.25.63
preprint arXiv:0801.2658 [math.AP]
- P. Colli & A. Segatti,
Uniform attractors for a phase transition model coupling
momentum balance and phase dynamics,
Discrete Contin. Dyn. Syst. 22 (2008), 909-932
doi:10.3934/dcds.2008.22.909
- E. Bonetti, P. Colli, M. Fabrizio & G. Gilardi,
Modelling and long-time behaviour for phase transitions
with entropy balance and thermal memory conductivity,
Discrete Contin. Dyn. Syst. Ser. B 6 (2006), 1001-1026
doi:10.3934/dcdsb.2006.6.1001
- P. Colli, M. Frémond, E. Rocca & K. Shirakawa,
Attractors
for a three-dimensional thermo-mechanical model of shape memory alloys,
Chinese Ann. Math. Ser. B 27 (2006), 683-700
doi:10.1007/s11401-005-0288-4
- E. Bonetti, P. Colli, M. Fabrizio & G. Gilardi,
Global solution to a singular integrodifferential system related to the
entropy balance,
Nonlinear Anal. 66 (2007), 1949-1979
doi:10.1016/j.na.2006.02.035
- P. Colli, P. Krejčí, E. Rocca & J. Sprekels,
Nonlinear evolution inclusions arising from phase change models,
Czechoslovak Math. J. 57 (2007), 1067-1098
doi:10.1007/s10587-007-0114-0
- P. Colli & P.I. Plotnikov,
Global solution
to a quasistationary Penrose–Fife model,
Indiana Univ. Math. J. 54
(2005), 349-382
doi:10.1512/iumj.2005.54.2595