Finite dimensional exponential attractor for the phase field model. (English) Zbl 0790.35052

Brochet, D.; Hilhorst, D.; Chen, Xinfu

Appl. Anal. 49, No. 3-4, 197-212 (1993).

We consider the phase field equations in arbitrary space dimension. We show that the corresponding boundary value problems are well-posed when assuming that the initial data is square integrable and prove the existence of a maximal attractor and of an inertial set.

Reviewer: X.Chen (Pittsburgh)

MSC:

35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K50	Systems of parabolic equations, boundary value problems (MSC2000)
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

Neumann boundary conditions; periodic boundary conditions; Dirichlet boundary conditions; semigroup; phase field equations; boundary value problems; maximal attractor; inertial set

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