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

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.

MSC:

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