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

Brochet, D.; Hilhorst, D.

Appl. Math. Lett. 4, No. 6, 59-62 (1991).

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.

MSC:

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

Keywords:

Neumann boundary conditions; periodic boundary conditions; Dirichlet conditions; phase field equations; existence of a universal attractor

References:

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