Universal attractor and inertial sets for the phase field model. (English) Zbl 0773.35028

Summary: We consider the phase field equations in dimensions 1, 2 and 3. We show that it is well-posed when assuming that the initial data is square integrable and prove the existence of a universal attractor and of inertial sets.


35K50 Systems of parabolic equations, boundary value problems (MSC2000)
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
35K45 Initial value problems for second-order parabolic systems
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