Sprekels, Jürgen; Tröltzsch, Fredi Second-order sufficient conditions in the sparse optimal control of a phase field tumor growth model with logarithmic potential. (English) Zbl 07815230 ESAIM, Control Optim. Calc. Var. 30, Paper No. 13, 25 p. (2024). MSC: 35K57 35K51 35Q93 37N25 49J50 49J52 49K20 49K40 PDFBibTeX XMLCite \textit{J. Sprekels} and \textit{F. Tröltzsch}, ESAIM, Control Optim. Calc. Var. 30, Paper No. 13, 25 p. (2024; Zbl 07815230) Full Text: DOI arXiv
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; 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; 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
Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen Analysis of a tumor model as a multicomponent deformable porous medium. (English) Zbl 1490.76207 Interfaces Free Bound. 24, No. 2, 235-262 (2022). MSC: 76S05 74N30 PDFBibTeX XMLCite \textit{P. Krejčí} et al., Interfaces Free Bound. 24, No. 2, 235--262 (2022; Zbl 1490.76207) 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
Sprekels, Jürgen; Tröltzsch, Fredi Sparse optimal control of a phase field system with singular potentials arising in the modeling of tumor growth. (English) Zbl 1475.35365 ESAIM, Control Optim. Calc. Var. 27, Suppl., Paper No. S26, 27 p. (2021). Reviewer: Gabriela Marinoschi (Bucureşti) MSC: 35Q92 35K57 37N25 49K20 92C17 92C37 PDFBibTeX XMLCite \textit{J. Sprekels} and \textit{F. Tröltzsch}, ESAIM, Control Optim. Calc. Var. 27, Paper No. S26, 27 p. (2021; Zbl 1475.35365) 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; 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
Frigeri, S.; Gal, C. G.; Grasselli, M.; Sprekels, J. Two-dimensional nonlocal Cahn-Hilliard-Navier-Stokes systems with variable viscosity, degenerate mobility and singular potential. (English) Zbl 1408.35149 Nonlinearity 32, No. 2, 678-727 (2019). MSC: 35Q35 37L30 45K05 76D03 76T99 35D35 35B65 35B41 PDFBibTeX XMLCite \textit{S. Frigeri} et al., Nonlinearity 32, No. 2, 678--727 (2019; Zbl 1408.35149) Full Text: DOI
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
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
Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen Unsaturated deformable porous media flow with thermal phase transition. (English) Zbl 1386.76163 Math. Models Methods Appl. Sci. 27, No. 14, 2675-2710 (2017). MSC: 76S05 82B26 74G25 PDFBibTeX XMLCite \textit{P. Krejčí} et al., Math. Models Methods Appl. Sci. 27, No. 14, 2675--2710 (2017; Zbl 1386.76163) 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
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
Rocca, E.; Sprekels, J. Optimal distributed control of a nonlocal convective Cahn-Hilliard equation by the velocity in three dimensions. (English) Zbl 1322.49006 SIAM J. Control Optim. 53, No. 3, 1654-1680 (2015). Reviewer: Gheorghe Aniculăesei (Iaşi) MSC: 49J20 49K20 35R09 45K05 74N99 PDFBibTeX XMLCite \textit{E. Rocca} and \textit{J. Sprekels}, SIAM J. Control Optim. 53, No. 3, 1654--1680 (2015; Zbl 1322.49006) Full Text: DOI arXiv Link
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