Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on R~N

摘要

We prove the existence of global attractors for the following semilinear degenerate parabolic equation on R~N: (?u)/(?t) - div (σ(x)▽u) + λu + f(x, u) = g(x), under a new condition concerning the variable nonnegative diffusivity σ(·) and for an arbitrary polynomial growth order of the nonlinearity f. To overcome some difficulties caused by the lack of compactness of the embeddings, these results are proved by combining the tail estimates method and the asymptotic a priori estimate method.