Pierluigi Colli, publications

COMPLETE LIST OF PUBLICATIONS

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RECENT PAPERS

( updated November 20, 2025 )

P. Colli, G. Gilardi, A. Signori & J. Sprekels,
On Brinkman flows with curvature-induced phase separation in binary mixtures,
preprint arXiv:2509.20282 [math.AP] (2025) 1-29

G. Cavalleri, P. Colli & E. Rocca,
Well-posedness for a fourth-order nonisothermal tumor growth model of Caginalp type,
preprint arXiv:2508.07979 [math.AP] (2025) 1-35

P. Colli & T. Fukao,
Asymptotic analysis of the Allen–Cahn equation with dynamic boundary conditions of Cahn–Hilliard type,
preprint arXiv:2508.02021 [math.AP] (2025) 1-35

P. Colli & G. Gilardi,
Hyperbolic relaxation of a sixth-order Cahn–Hilliard equation,
Discrete Contin. Dyn. Syst. Ser. S Early access (2025)
doi:10.3934/dcdss.2025106 preprint arXiv:2504.03580 [math.AP] (2025) 1-25

P. Colli & J. Sprekels,
On the optimal control of viscous Cahn–Hilliard systems with hyperbolic relaxation of the chemical potential,
Commun. Anal. Mech. 17 (2025), 683-706
doi:10.3934/cam.2025027 preprint arXiv:2503.15444 [math.OC] (2025)

P. Colli & S. Kurima,
Analysis of a nonisothermal and conserved phase field system with inertial term,
J. Math. Anal. Appl. 552 (2025), no. 1, Paper No. 129744, 24 pp.
doi:10.1016/j.jmaa.2025.129744 preprint arXiv:2502.13600 [math.AP] (2025)

G. Cavalleri, P. Colli, A. Miranville & E. Rocca,
On a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage,
Nonlinear Anal. Real World Appl. 87 (2026), Paper No. 104419, 18 pp.
doi:10.1016/j.nonrwa.2025.104419 preprint arXiv:2502.02126 [math.AP] (2025)

P. Colli & J. Sprekels,
Hyperbolic relaxation of the chemical potential in the viscous Cahn–Hilliard equation,
in `Advances in Continuum Physics –– In Memoriam Wolfgang Dreyer',
J. Fuhrmann, D. Hömberg, W. H. Müller, W. Weiss (ed.),
Adv. Struct. Mater. 238, Springer, Cham, 2025, pp. 529-556
doi:10.1007/978-3-031-93918-1_18 preprint arXiv:2408.16332 [math.AP] (2024)

P. Colli, G. Gilardi, A. Signori & J. Sprekels,
Solvability and optimal control of a multi-species Cahn–Hilliard–Keller–Segel tumor growth model,
ESAIM Control Optim. Calc. Var. 31 (2025), Paper No. 85, 37 pp.
doi:10.1051/cocv/2025070 preprint arXiv:2407.18162 [math.AP] (2024)

P. Colli & J. Sprekels,
Second-order optimality conditions for the sparse optimal control of nonviscous Cahn–Hilliard systems,
preprint arXiv:2406.02384 [math.OC] (2024) 1-40

P. Colli, G. Marinoschi, E. Rocca & A. Viguerie,
Chemotaxis-inspired PDE model for airborne infectious disease transmission: analysis and simulations,
J. Nonlinear Sci. 35 (2025), no. 1, Paper No. 28, 38 pp.
doi:10.1007/s00332-024-10121-8 preprint arXiv:2404.17506 [q-bio.PE] (2024)

P. Colli, J. Sprekels & F. Tröltzsch,
Optimality conditions for sparse optimal control of viscous Cahn–Hilliard systems with logarithmic potential,
Appl. Math. Optim. 90 (2024), no. 2, Paper No. 47, 48 pp.
doi:10.1007/s00245-024-10187-6 preprint arXiv:2402.18506 [math.OC] (2024)

P. Colli, S. Kurima & L. Scarpa,
Nonlocal to local convergence of phase field systems with inertial term,
Appl. Math. Optim. 90 (2024), no. 1, Paper No. 21, 16 pp.
doi:10.1007/s00245-024-10166-x preprint arXiv:2402.12145 [math.AP] (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,
SIAM J. Math. Anal. 56 (2024), 4928-4969
doi:10.1137/24M1630372 preprint arXiv:2401.05189 [math.AP] (2024)

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,
J. Evol. Equ. 24 (2024), no. 4, Paper No. 85, 55 pp.
doi:10.1007/s00028-024-00999-y preprint arXiv:2312.15274 [math.AP] (2023)

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, Paper No. 28, 27 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,
J. Nonlinear Sci. 35 (2025), no. 4, Paper No. 73, 47 pp.
doi:10.1007/s00332-025-10168-1 preprint arXiv:2307.02992 [math.AP] (2023)

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), no. 2, 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

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