Colli, Pierluigi; Hilhorst, Danielle; Issard-Roch, Françoise; Schimperna, Giulio Long time convergence for a class of variational phase-field models. (English) Zbl 1178.35065 Discrete Contin. Dyn. Syst. 25, No. 1, 63-81 (2009). Summary: We analyze a class of phase field models for the dynamics of phase transitions which extend the well-known Caginalp and Penrose-Fife phase field models. We prove the existence and uniqueness of the solution of a corresponding initial boundary value problem and deduce further regularity of the solution by exploiting the so-called regularizing effect. Finally we study the long time behavior of the solution and show that it converges algebraically fast to a stationary solution as \(t\) tends to infinity. Cited in 5 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 80A22 Stefan problems, phase changes, etc. 35K51 Initial-boundary value problems for second-order parabolic systems 35K55 Nonlinear parabolic equations Keywords:gradient flow; \(\omega\)-limit set; Simon-Lojasiewicz inequality; existence; uniqueness; regularity; regularizing effect PDFBibTeX XMLCite \textit{P. Colli} et al., Discrete Contin. Dyn. Syst. 25, No. 1, 63--81 (2009; Zbl 1178.35065) Full Text: DOI arXiv