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Long-time behavior for a class of degenerate parabolic equations. (English) Zbl 1292.74015

Summary: The long-time behavior of a class of degenerate parabolic equations in a bounded domain will be considered in the sense that the nonnegative diffusion coefficient \(a(x)\) is allowed to vanish on a nonempty closed subset with zero measure. For this purpose, some appropriate weighted Sobolev spaces are introduced and the corresponding embedding theorem is established. Then, we show the global existence and uniqueness of weak solutions. Finally, we distinguish two cases (subcritical and supcritical) to prove the existence of compact attractors for the semigroup associated with this class of equations.

MSC:

74H40 Long-time behavior of solutions for dynamical problems in solid mechanics
35B41 Attractors
35K65 Degenerate parabolic equations
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