Miranville, Alain An Allen-Cahn equation based on an unconstrained order parameter and its Cahn-Hilliard limit. (English) Zbl 1472.35025 J. Math. Anal. Appl. 504, No. 2, Article ID 125486, 17 p. (2021). MSC: 35B25 35K35 35K58 PDFBibTeX XMLCite \textit{A. Miranville}, J. Math. Anal. Appl. 504, No. 2, Article ID 125486, 17 p. (2021; Zbl 1472.35025) Full Text: DOI
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 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
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
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
Thomas, Marita Uniform Poincaré-Sobolev and isoperimetric inequalities for classes of domains. (English) Zbl 1348.46043 Discrete Contin. Dyn. Syst. 35, No. 6, 2741-2761 (2015). MSC: 46E35 26D10 52A38 PDFBibTeX XMLCite \textit{M. Thomas}, Discrete Contin. Dyn. Syst. 35, No. 6, 2741--2761 (2015; Zbl 1348.46043) Full Text: DOI
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
Shin, Jaemin; Choi, Yongho; Kim, Junseok An unconditionally stable numerical method for the viscous Cahn-Hilliard equation. (English) Zbl 1304.65205 Discrete Contin. Dyn. Syst., Ser. B 19, No. 6, 1737-1747 (2014). MSC: 65M12 65M06 65M55 35Q35 PDFBibTeX XMLCite \textit{J. Shin} et al., Discrete Contin. Dyn. Syst., Ser. B 19, No. 6, 1737--1747 (2014; Zbl 1304.65205) Full Text: DOI
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