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

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
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