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
Acosta-Soba, Daniel; Guillén-González, Francisco; Rodríguez-Galván, J. Rafael A structure-preserving upwind DG scheme for a degenerate phase-field tumor model. (English) Zbl 07801666 Comput. Math. Appl. 152, 317-333 (2023). MSC: 76-XX 82-XX PDFBibTeX XMLCite \textit{D. Acosta-Soba} et al., Comput. Math. Appl. 152, 317--333 (2023; Zbl 07801666) Full Text: DOI arXiv
Zhao, Xiaopeng Optimal distributed control of two-dimensional Navier-Stokes-Cahn-Hilliard system with chemotaxis and singular potential. (English) Zbl 1520.76109 Appl. Math. Optim. 88, No. 1, Paper No. 2, 37 p. (2023). MSC: 76Z05 76D55 76T06 76D05 92C17 PDFBibTeX XMLCite \textit{X. Zhao}, Appl. Math. Optim. 88, No. 1, Paper No. 2, 37 p. (2023; Zbl 1520.76109) Full Text: DOI
Rocca, Elisabetta; Schimperna, Giulio; Signori, Andrea On a Cahn-Hilliard-Keller-Segel model with generalized logistic source describing tumor growth. (English) Zbl 1502.35044 J. Differ. Equations 343, 530-578 (2023). MSC: 35D30 35K35 35K51 35K86 92C17 92C50 PDFBibTeX XMLCite \textit{E. Rocca} et al., J. Differ. Equations 343, 530--578 (2023; Zbl 1502.35044) Full Text: DOI arXiv
Alsayed, Hawraa; Fakih, Hussein; Miranville, Alain; Wehbe, Ali Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs. (English) Zbl 1514.92039 Discrete Contin. Dyn. Syst., Ser. S 15, No. 12, 3481-3515 (2022). MSC: 92C50 35K20 35Q93 49K20 49N90 PDFBibTeX XMLCite \textit{H. Alsayed} et al., Discrete Contin. Dyn. Syst., Ser. S 15, No. 12, 3481--3515 (2022; Zbl 1514.92039) Full Text: DOI
Frigeri, Sergio; Lam, Kei Fong; Signori, Andrea Strong well-posedness and inverse identification problem of a non-local phase field tumour model with degenerate mobilities. (English) Zbl 1504.35128 Eur. J. Appl. Math. 33, No. 2, 267-308 (2022). MSC: 35D30 35K52 35K58 35R30 49J20 92C50 PDFBibTeX XMLCite \textit{S. Frigeri} et al., Eur. J. Appl. Math. 33, No. 2, 267--308 (2022; Zbl 1504.35128) 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; 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
Biswas, Tania; Rocca, Elisabetta Long time dynamics of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects. (English) Zbl 1496.35394 Discrete Contin. Dyn. Syst., Ser. B 27, No. 5, 2455-2469 (2022). Reviewer: Catalin Popa (Iaşi) MSC: 35Q92 92C50 92C37 92C35 35K58 35K51 35B41 37L30 PDFBibTeX XMLCite \textit{T. Biswas} and \textit{E. Rocca}, Discrete Contin. Dyn. Syst., Ser. B 27, No. 5, 2455--2469 (2022; Zbl 1496.35394) Full Text: DOI arXiv
Sakthivel, K.; Arivazhagan, A.; Barani Balan, N. Inverse problem for a Cahn-Hilliard type system modeling tumor growth. (English) Zbl 1485.35426 Appl. Anal. 101, No. 3, 858-890 (2022). MSC: 35R30 35B35 35K51 35K58 35Q92 PDFBibTeX XMLCite \textit{K. Sakthivel} et al., Appl. Anal. 101, No. 3, 858--890 (2022; Zbl 1485.35426) Full Text: DOI
Knopf, Patrik; Signori, Andrea Existence of weak solutions to multiphase Cahn-Hilliard-Darcy and Cahn-Hilliard-Brinkman models for stratified tumor growth with chemotaxis and general source terms. (English) Zbl 1484.35148 Commun. Partial Differ. Equations 47, No. 2, 233-278 (2022). MSC: 35D30 35K35 35K86 76D07 92C17 92C50 PDFBibTeX XMLCite \textit{P. Knopf} and \textit{A. Signori}, Commun. Partial Differ. Equations 47, No. 2, 233--278 (2022; Zbl 1484.35148) Full Text: DOI arXiv
Giorgini, Andrea; Lam, Kei Fong; Rocca, Elisabetta; Schimperna, Giulio On the existence of strong solutions to the Cahn-Hilliard-Darcy system with mass source. (English) Zbl 1482.35071 SIAM J. Math. Anal. 54, No. 1, 737-767 (2022). MSC: 35D35 35K61 35Q35 76D27 PDFBibTeX XMLCite \textit{A. Giorgini} et al., SIAM J. Math. Anal. 54, No. 1, 737--767 (2022; Zbl 1482.35071) Full Text: DOI arXiv
Rocca, Elisabetta; Scarpa, Luca; Signori, Andrea Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis. (English) Zbl 1482.35277 Math. Models Methods Appl. Sci. 31, No. 13, 2643-2694 (2021). MSC: 35R30 35B40 49J50 92B05 92C17 PDFBibTeX XMLCite \textit{E. Rocca} et al., Math. Models Methods Appl. Sci. 31, No. 13, 2643--2694 (2021; Zbl 1482.35277) 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
Scarpa, Luca The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit. (English) Zbl 1470.35452 Appl. Math. Optim. 84, No. 1, 487-533 (2021). MSC: 35R60 35B25 35K35 60H15 80A22 PDFBibTeX XMLCite \textit{L. Scarpa}, Appl. Math. Optim. 84, No. 1, 487--533 (2021; Zbl 1470.35452) 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
Signori, Andrea Penalisation of long treatment time and optimal control of a tumour growth model of Cahn-Hilliard type with singular potential. (English) Zbl 1470.35369 Discrete Contin. Dyn. Syst. 41, No. 6, 2519-2542 (2021). MSC: 35Q92 49J20 49K20 35K86 92C50 92C37 92C17 PDFBibTeX XMLCite \textit{A. Signori}, Discrete Contin. Dyn. Syst. 41, No. 6, 2519--2542 (2021; Zbl 1470.35369) Full Text: DOI arXiv
Scarpa, Luca; Signori, Andrea On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport. (English) Zbl 1468.35217 Nonlinearity 34, No. 5, 3199-3250 (2021). MSC: 35Q92 92C17 35K86 35K61 35K57 35D35 35B40 35B65 35A01 35A02 65J99 35R09 PDFBibTeX XMLCite \textit{L. Scarpa} and \textit{A. Signori}, Nonlinearity 34, No. 5, 3199--3250 (2021; Zbl 1468.35217) Full Text: DOI arXiv Link
Cavaterra, Cecilia; Rocca, Elisabetta; Wu, Hao Long-time dynamics and optimal control of a diffuse interface model for tumor growth. (English) Zbl 1464.35357 Appl. Math. Optim. 83, No. 2, 739-787 (2021). MSC: 35Q92 92C17 92C37 92C50 35K61 49J20 49K20 49N90 35B35 PDFBibTeX XMLCite \textit{C. Cavaterra} et al., Appl. Math. Optim. 83, No. 2, 739--787 (2021; Zbl 1464.35357) Full Text: DOI arXiv Link
Garcke, Harald; Lam, Kei Fong; Signori, Andrea On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects. (English) Zbl 1456.35091 Nonlinear Anal., Real World Appl. 57, Article ID 103192, 28 p. (2021). Reviewer: Joseph Shomberg (Providence) MSC: 35G61 49J20 35Q92 PDFBibTeX XMLCite \textit{H. Garcke} et al., Nonlinear Anal., Real World Appl. 57, Article ID 103192, 28 p. (2021; Zbl 1456.35091) 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
Signori, Andrea Optimal distributed control of an extended model of tumor growth with logarithmic potential. (English) Zbl 1448.35521 Appl. Math. Optim. 82, No. 2, 517-549 (2020). MSC: 35Q92 35K61 92C37 49J20 49K20 92C50 PDFBibTeX XMLCite \textit{A. Signori}, Appl. Math. Optim. 82, No. 2, 517--549 (2020; Zbl 1448.35521) Full Text: DOI arXiv
Signori, Andrea Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme. (English) Zbl 1453.35032 Math. Control Relat. Fields 10, No. 2, 305-331 (2020). Reviewer: Vyacheslav I. Maksimov (Yekaterinburg) MSC: 35B40 35K61 49J20 49K20 35K86 92C50 35Q93 PDFBibTeX XMLCite \textit{A. Signori}, Math. Control Relat. Fields 10, No. 2, 305--331 (2020; Zbl 1453.35032) 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
Signori, Andrea Optimality conditions for an extended tumor growth model with double obstacle potential via deep quench approach. (English) Zbl 1431.35079 Evol. Equ. Control Theory 9, No. 1, 193-217 (2020). MSC: 35K61 35Q92 49J20 49K20 35K86 92C50 PDFBibTeX XMLCite \textit{A. Signori}, Evol. Equ. Control Theory 9, No. 1, 193--217 (2020; Zbl 1431.35079) 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
Miranville, Alain; Rocca, Elisabetta; Schimperna, Giulio On the long time behavior of a tumor growth model. (English) Zbl 1416.35279 J. Differ. Equations 267, No. 4, 2616-2642 (2019). MSC: 35Q92 35D30 35K57 35B41 37L30 35B40 92C37 PDFBibTeX XMLCite \textit{A. Miranville} et al., J. Differ. Equations 267, No. 4, 2616--2642 (2019; Zbl 1416.35279) Full Text: DOI arXiv
Garcke, Harald; Lam, Kei Fong; Rocca, Elisabetta Optimal control of treatment time in a diffuse interface model of tumor growth. (English) Zbl 1403.35139 Appl. Math. Optim. 78, No. 3, 495-544 (2018). MSC: 35K61 49J20 49K20 92C37 92C50 PDFBibTeX XMLCite \textit{H. Garcke} et al., Appl. Math. Optim. 78, No. 3, 495--544 (2018; Zbl 1403.35139) Full Text: DOI arXiv
Miranville, Alain The Cahn-Hilliard equation and some of its variants. (English) Zbl 1425.35086 AIMS Math. 2, No. 3, 479-544 (2017). MSC: 35K55 35B45 PDFBibTeX XMLCite \textit{A. Miranville}, AIMS Math. 2, No. 3, 479--544 (2017; Zbl 1425.35086) Full Text: DOI
Garcke, Harald; Lam, Kei Fong Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. (English) Zbl 1375.92011 Eur. J. Appl. Math. 28, No. 2, 284-316 (2017). MSC: 92C17 92C50 35B30 35K57 35Q92 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{K. F. Lam}, Eur. J. Appl. Math. 28, No. 2, 284--316 (2017; Zbl 1375.92011) Full Text: DOI arXiv
Rocca, Elisabetta; Scala, Riccardo A rigorous sharp interface limit of a diffuse interface model related to tumor growth. (English) Zbl 1370.92076 J. Nonlinear Sci. 27, No. 3, 847-872 (2017). Reviewer: Andrzej Świerniak (Gliwice) MSC: 92C50 82B24 82B21 49J40 92C17 35K57 35R11 PDFBibTeX XMLCite \textit{E. Rocca} and \textit{R. Scala}, J. Nonlinear Sci. 27, No. 3, 847--872 (2017; Zbl 1370.92076) Full Text: DOI arXiv
Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E. Analysis of a diffuse interface model of multispecies tumor growth. (English) Zbl 1367.35185 Nonlinearity 30, No. 4, 1639-1658 (2017). MSC: 35Q92 35B25 35D30 35K35 35K57 74G25 78A70 92C17 92C37 76S05 35Q35 PDFBibTeX XMLCite \textit{M. Dai} et al., Nonlinearity 30, No. 4, 1639--1658 (2017; Zbl 1367.35185) Full Text: DOI arXiv
Garcke, Harald; Lam, Kei Fong Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth. (English) Zbl 1434.35255 AIMS Math. 1, No. 3, 318-360 (2016). MSC: 35Q92 92C37 92C17 35Q35 76S05 35D30 35B65 35B40 PDFBibTeX XMLCite \textit{H. Garcke} and \textit{K. F. Lam}, AIMS Math. 1, No. 3, 318--360 (2016; Zbl 1434.35255) Full Text: DOI arXiv