Colli, Pierluigi; Gilardi, Gianni; Signori, Andrea; Sprekels, Jürgen On a Cahn-Hilliard system with source term and thermal memory. (English) Zbl 07792514 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 240, Article ID 113461, 16 p. (2024). MSC: 35K52 35K58 PDFBibTeX XMLCite \textit{P. Colli} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 240, Article ID 113461, 16 p. (2024; Zbl 07792514) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Marinoschi, Gabriela Global solution and optimal control of an epidemic propagation with a heterogeneous diffusion. (English) Zbl 07791685 Appl. Math. Optim. 89, No. 1, Paper No. 28, 27 p. (2024). MSC: 35K51 35K57 46N60 49J20 49J50 49K20 92D30 PDFBibTeX XMLCite \textit{P. Colli} et al., Appl. Math. Optim. 89, No. 1, Paper No. 28, 27 p. (2024; Zbl 07791685) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Marinoschi, Gabriela; Rocca, Elisabetta Optimal control of a reaction-diffusion model related to the spread of COVID-19. (English) Zbl 07785848 Anal. Appl., Singap. 22, No. 1, 111-136 (2024). MSC: 35Q92 92D30 35K55 35K57 46N60 49J20 35A01 35A02 PDFBibTeX XMLCite \textit{P. Colli} et al., Anal. Appl., Singap. 22, No. 1, 111--136 (2024; Zbl 07785848) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Signori, Andrea; Sprekels, Jürgen Optimal control of a nonconserved phase field model of Caginalp type with thermal memory and double obstacle potential. (English) Zbl 1526.49002 Discrete Contin. Dyn. Syst., Ser. S 16, No. 9, 2305-2325 (2023). MSC: 49J20 49K20 35K55 35K51 49J50 PDFBibTeX XMLCite \textit{P. Colli} et al., Discrete Contin. Dyn. Syst., Ser. S 16, No. 9, 2305--2325 (2023; Zbl 1526.49002) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Signori, Andrea; Sprekels, Jürgen Optimal temperature distribution for a nonisothermal Cahn-Hilliard system with source term. (English) Zbl 1522.35309 Appl. Math. Optim. 88, No. 2, Paper No. 68, 31 p. (2023). MSC: 35K55 35K51 35G61 49J20 49K20 49J50 35Q93 PDFBibTeX XMLCite \textit{P. Colli} et al., Appl. Math. Optim. 88, No. 2, Paper No. 68, 31 p. (2023; Zbl 1522.35309) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Rocca, Elisabetta; Sprekels, Jürgen Well-posedness and optimal control for a Cahn-Hilliard-Oono system with control in the mass term. (English) Zbl 1500.35200 Discrete Contin. Dyn. Syst., Ser. S 15, No. 8, 2135-2172 (2022). MSC: 35K52 35K58 35D35 49J20 49K30 35Q93 PDFBibTeX XMLCite \textit{P. Colli} et al., Discrete Contin. Dyn. Syst., Ser. S 15, No. 8, 2135--2172 (2022; Zbl 1500.35200) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen Well-posedness for a class of phase-field systems modeling prostate cancer growth with fractional operators and general nonlinearities. (English) Zbl 1493.35123 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 33, No. 1, 193-228 (2022). MSC: 35Q92 35R11 35K51 PDFBibTeX XMLCite \textit{P. Colli} et al., Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 33, No. 1, 193--228 (2022; Zbl 1493.35123) Full Text: DOI arXiv
Colli, Pierluigi; Fukao, Takeshi; Scarpa, Luca The Cahn-Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity. (English) Zbl 1504.35063 SIAM J. Math. Anal. 54, No. 3, 3292-3315 (2022). Reviewer: Gabriela Marinoschi (Bucureşti) MSC: 35B40 35K61 35K35 35K58 35D30 35B20 74N20 80A22 PDFBibTeX XMLCite \textit{P. Colli} et al., SIAM J. Math. Anal. 54, No. 3, 3292--3315 (2022; Zbl 1504.35063) Full Text: DOI arXiv
Colli, Pierluigi; Signori, Andrea; Sprekels, Jürgen Optimal control problems with sparsity for tumor growth models involving variational inequalities. (English) Zbl 1492.92014 J. Optim. Theory Appl. 194, No. 1, 25-58 (2022). MSC: 92C32 92C17 49J40 49J20 35K57 PDFBibTeX XMLCite \textit{P. Colli} et al., J. Optim. Theory Appl. 194, No. 1, 25--58 (2022; Zbl 1492.92014) Full Text: DOI arXiv
Colli, Pierluigi; Signori, Andrea; Sprekels, Jürgen Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis. (English) Zbl 1473.49053 ESAIM, Control Optim. Calc. Var. 27, Paper No. 73, 46 p. (2021). MSC: 49S05 92C17 92C37 49J20 49K20 49K40 35K57 37N25 PDFBibTeX XMLCite \textit{P. Colli} et al., ESAIM, Control Optim. Calc. Var. 27, Paper No. 73, 46 p. (2021; Zbl 1473.49053) Full Text: DOI arXiv
Colli, Pierluigi; Signori, Andrea; Sprekels, Jürgen Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials. (English) Zbl 1486.35392 Appl. Math. Optim. 83, No. 3, 2017-2049 (2021); correction ibid. 84, No. 3, 3569-3570 (2021). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q92 49K20 35K58 49K40 92C37 92C50 35B65 PDFBibTeX XMLCite \textit{P. Colli} et al., Appl. Math. Optim. 83, No. 3, 2017--2049 (2021; Zbl 1486.35392) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen Asymptotic analysis of a tumor growth model with fractional operators. (English) Zbl 1476.35284 Asymptotic Anal. 120, No. 1-2, 41-72 (2020). Reviewer: Catalin Popa (Iaşi) MSC: 35Q92 92C37 92C17 35A01 35A02 35B65 35B40 26A33 35R11 PDFBibTeX XMLCite \textit{P. Colli} et al., Asymptotic Anal. 120, No. 1--2, 41--72 (2020; Zbl 1476.35284) Full Text: DOI arXiv
Colli, Pierluigi; Fukao, Takeshi Vanishing diffusion in a dynamic boundary condition for the Cahn-Hilliard equation. (English) Zbl 1452.35080 NoDEA, Nonlinear Differ. Equ. Appl. 27, No. 6, Paper No. 53, 26 p. (2020). MSC: 35K61 35K35 35K58 74N20 80A22 35B25 PDFBibTeX XMLCite \textit{P. Colli} and \textit{T. Fukao}, NoDEA, Nonlinear Differ. Equ. Appl. 27, No. 6, Paper No. 53, 26 p. (2020; Zbl 1452.35080) Full Text: DOI arXiv
Bonetti, Elena; Colli, Pierluigi; Scarpa, Luca; Tomassetti, Giuseppe Bounded solutions and their asymptotics for a doubly nonlinear Cahn-Hilliard system. (English) Zbl 1445.35053 Calc. Var. Partial Differ. Equ. 59, No. 2, Paper No. 88, 25 p. (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 35B40 35K52 35B25 35D35 35G31 74N20 74N25 PDFBibTeX XMLCite \textit{E. Bonetti} et al., Calc. Var. Partial Differ. Equ. 59, No. 2, Paper No. 88, 25 p. (2020; Zbl 1445.35053) Full Text: DOI arXiv
Colli, Pierluigi; Kurima, Shunsuke Time discretization of a nonlinear phase field system in general domains. (English) Zbl 1480.35008 Commun. Pure Appl. Anal. 18, No. 6, 3161-3179 (2019). MSC: 35A35 35K51 82B26 PDFBibTeX XMLCite \textit{P. Colli} and \textit{S. Kurima}, Commun. Pure Appl. Anal. 18, No. 6, 3161--3179 (2019; Zbl 1480.35008) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen Nonlocal phase field models of viscous Cahn-Hilliard type. (English) Zbl 1448.35285 Hintermüller, Michael (ed.) et al., Topics in applied analysis and optimisation. Partial differential equations, stochastic and numerical analysis. Selected papers from the Joint CIM-WIAS workshop, TAAO’17, Lisbon, Portugal, December 6–8, 2017. Cham: Springer. CIM Ser. Math. Sci, 71-100 (2019). MSC: 35K35 35K59 35Q93 PDFBibTeX XMLCite \textit{P. Colli} et al., in: Topics in applied analysis and optimisation. Partial differential equations, stochastic and numerical analysis. Selected papers from the Joint CIM-WIAS workshop, TAAO'17, Lisbon, Portugal, December 6--8, 2017. Cham: Springer. 71--100 (2019; Zbl 1448.35285) Full Text: DOI
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen Well-posedness and regularity for a generalized fractional Cahn-Hilliard system. (English) Zbl 1437.35425 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 30, No. 3, 437-478 (2019). Reviewer: Mohammed El Aïdi (Bogotá) MSC: 35K45 35K90 35R11 PDFBibTeX XMLCite \textit{P. Colli} et al., Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 30, No. 3, 437--478 (2019; Zbl 1437.35425) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Marinoschi, Gabriela; Rocca, Elisabetta Sliding mode control for a phase field system related to tumor growth. (English) Zbl 1420.35434 Appl. Math. Optim. 79, No. 3, 647-670 (2019). MSC: 35Q92 35K25 35K61 93B52 92C50 97M60 92C37 PDFBibTeX XMLCite \textit{P. Colli} et al., Appl. Math. Optim. 79, No. 3, 647--670 (2019; Zbl 1420.35434) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen On a Cahn-Hilliard system with convection and dynamic boundary conditions. (English) Zbl 1406.35163 Ann. Mat. Pura Appl. (4) 197, No. 5, 1445-1475 (2018). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35K61 35K25 76R05 80A22 PDFBibTeX XMLCite \textit{P. Colli} et al., Ann. Mat. Pura Appl. (4) 197, No. 5, 1445--1475 (2018; Zbl 1406.35163) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen On the longtime behavior of a viscous Cahn-Hilliard system with convection and dynamic boundary conditions. (English) Zbl 1404.35044 J. Elliptic Parabol. Equ. 4, No. 2, 327-347 (2018). MSC: 35B40 47J20 74N25 35G55 PDFBibTeX XMLCite \textit{P. Colli} et al., J. Elliptic Parabol. Equ. 4, No. 2, 327--347 (2018; Zbl 1404.35044) Full Text: DOI arXiv
Bonetti, Elena; Colli, Pierluigi; Scarpa, Luca; Tomassetti, Giuseppe A doubly nonlinear Cahn-Hilliard system with nonlinear viscosity. (English) Zbl 1393.35235 Commun. Pure Appl. Anal. 17, No. 3, 1001-1022 (2018). MSC: 35Q74 35G31 35K52 35D35 74N20 PDFBibTeX XMLCite \textit{E. Bonetti} et al., Commun. Pure Appl. Anal. 17, No. 3, 1001--1022 (2018; Zbl 1393.35235) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen Optimal boundary control of a nonstandard viscous Cahn-Hilliard system with dynamic boundary condition. (English) Zbl 1390.35168 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 170, 171-196 (2018). MSC: 35K61 49J20 49J50 49K20 PDFBibTeX XMLCite \textit{P. Colli} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 170, 171--196 (2018; Zbl 1390.35168) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Nakayashiki, Ryota; Shirakawa, Ken A class of quasi-linear Allen-Cahn type equations with dynamic boundary conditions. (English) Zbl 1372.35162 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 158, 32-59 (2017). MSC: 35K61 35K55 35K59 82C26 35B30 PDFBibTeX XMLCite \textit{P. Colli} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 158, 32--59 (2017; Zbl 1372.35162) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen Global existence for a nonstandard viscous Cahn-Hilliard system with dynamic boundary condition. (English) Zbl 1365.35059 SIAM J. Math. Anal. 49, No. 3, 1732-1760 (2017). MSC: 35K52 35K61 35A01 35B40 74A15 PDFBibTeX XMLCite \textit{P. Colli} et al., SIAM J. Math. Anal. 49, No. 3, 1732--1760 (2017; Zbl 1365.35059) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Rocca, Elisabetta; Sprekels, Jürgen Asymptotic analyses and error estimates for a Cahn-Hilliard type phase field system modelling tumor growth. (English) Zbl 1360.35296 Discrete Contin. Dyn. Syst., Ser. S 10, No. 1, 37-54 (2017). Reviewer: Johannes Lankeit (Paderborn) MSC: 35Q92 92C17 35K57 78M35 35B20 65N15 92C50 35R35 PDFBibTeX XMLCite \textit{P. Colli} et al., Discrete Contin. Dyn. Syst., Ser. S 10, No. 1, 37--54 (2017; Zbl 1360.35296) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential. (English) Zbl 1364.35131 Evol. Equ. Control Theory 6, No. 1, 35-58 (2017). MSC: 35K55 49K20 74A15 35K25 35R70 PDFBibTeX XMLCite \textit{P. Colli} et al., Evol. Equ. Control Theory 6, No. 1, 35--58 (2017; Zbl 1364.35131) Full Text: DOI arXiv
Barbu, Viorel; Colli, Pierluigi; Gilardi, Gianni; Marinoschi, Gabriela Feedback stabilization of the Cahn-Hilliard type system for phase separation. (English) Zbl 1351.93113 J. Differ. Equations 262, No. 3, 2286-2334 (2017). MSC: 93D15 35K52 35Q79 35Q93 93C20 PDFBibTeX XMLCite \textit{V. Barbu} et al., J. Differ. Equations 262, No. 3, 2286--2334 (2017; Zbl 1351.93113) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen On an application of Tikhonov’s fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation. (English) Zbl 1335.35100 J. Differ. Equations 260, No. 11, 7940-7964 (2016). MSC: 35K40 35K86 45K05 47H10 80A22 PDFBibTeX XMLCite \textit{P. Colli} et al., J. Differ. Equations 260, No. 11, 7940--7964 (2016; Zbl 1335.35100) Full Text: DOI arXiv
Bonetti, Elena; Colli, Pierluigi; Fabrizio, Mauro; Gilardi, Gianni Existence of solutions for a mathematical model related to solid-solid phase transitions in shape memory alloys. (English) Zbl 1333.35271 Arch. Ration. Mech. Anal. 219, No. 1, 203-254 (2016). MSC: 35Q74 74N05 74D10 35B45 35K55 35D30 35B65 PDFBibTeX XMLCite \textit{E. Bonetti} et al., Arch. Ration. Mech. Anal. 219, No. 1, 203--254 (2016; Zbl 1333.35271) Full Text: DOI arXiv
Colli, Pierluigi; Fukao, Takeshi The Allen-Cahn equation with dynamic boundary conditions and mass constraints. (English) Zbl 1334.35165 Math. Methods Appl. Sci. 38, No. 17, 3950-3967 (2015). MSC: 35K86 49J40 80A22 35K57 PDFBibTeX XMLCite \textit{P. Colli} and \textit{T. Fukao}, Math. Methods Appl. Sci. 38, No. 17, 3950--3967 (2015; Zbl 1334.35165) Full Text: DOI arXiv
Colli, Pierluigi; Fukao, Takeshi Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials. (English) Zbl 1323.35092 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 127, 413-433 (2015). Reviewer: Mersaid Aripov (Tashkent) MSC: 35K61 35K25 35D30 35D35 80A22 PDFBibTeX XMLCite \textit{P. Colli} and \textit{T. Fukao}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 127, 413--433 (2015; Zbl 1323.35092) Full Text: DOI arXiv
Colli, Pierluigi; Fukao, Takeshi Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary. (English) Zbl 1327.35149 J. Math. Anal. Appl. 429, No. 2, 1190-1213 (2015). MSC: 35K35 35K86 PDFBibTeX XMLCite \textit{P. Colli} and \textit{T. Fukao}, J. Math. Anal. Appl. 429, No. 2, 1190--1213 (2015; Zbl 1327.35149) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Krejčí, Pavel; Sprekels, Jürgen A vanishing diffusion limit in a nonstandard system of phase field equations. (English) Zbl 1320.35172 Evol. Equ. Control Theory 3, No. 2, 257-275 (2014). MSC: 35K59 35K61 35A01 35B40 74A15 35K51 35A02 PDFBibTeX XMLCite \textit{P. Colli} et al., Evol. Equ. Control Theory 3, No. 2, 257--275 (2014; Zbl 1320.35172) Full Text: DOI arXiv
Colli, Pierluigi; Gilardi, Gianni; Podio-Guidugli, Paolo; Sprekels, Jürgen Global existence and uniqueness for a singular/degenerate Cahn-Hilliard system with viscosity. (English) Zbl 1325.35105 J. Differ. Equations 254, No. 11, 4217-4244 (2013). Reviewer: Josipa Pina Milišić (Zagreb) MSC: 35K61 35A01 35A02 74A15 74N25 35K65 35K67 PDFBibTeX XMLCite \textit{P. Colli} et al., J. Differ. Equations 254, No. 11, 4217--4244 (2013; Zbl 1325.35105) Full Text: DOI arXiv
Colli, Pierluigi; Frigeri, Sergio; Grasselli, Maurizio Global existence of weak solutions to a nonlocal Cahn-Hilliard-Navier-Stokes system. (English) Zbl 1241.35155 J. Math. Anal. Appl. 386, No. 1, 428-444 (2012). Reviewer: Titus Petrila (Cluj-Napoca) MSC: 35Q35 35D30 76D05 76D50 35R09 PDFBibTeX XMLCite \textit{P. Colli} et al., J. Math. Anal. Appl. 386, No. 1, 428--444 (2012; Zbl 1241.35155) Full Text: DOI arXiv