Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions. (English) Zbl 1244.35067

Conti, Monica; Gatti, Stefania; Miranville, Alain

Discrete Contin. Dyn. Syst., Ser. S 5, No. 3, 485-505 (2012).

The authors study the Caginalp system in phase transition with coupled dynamic boundary conditions in both variables. They prove that the system generates a strongly continuous semigroup in a certain phase-space. The existence of a finite dimensional global attractor and of an exponential attractor is also established.

Reviewer: Dumitru Motreanu (Perpignan)

MSC:

35K55	Nonlinear parabolic equations
35J60	Nonlinear elliptic equations
80A22	Stefan problems, phase changes, etc.
35B41	Attractors

Keywords:

Caginalp system; phase transition; dynamic boundary conditions; global attractor; exponential attractor