Dynamical behavior of a degenerate parabolic equation with memory on the whole space.

This paper is concerned with the existence and uniqueness of global attractors for a class of degenerate parabolic equations with memory on R n . Since the corresponding equation includes the degenerate term div { a (x) ∇ u } , it requires us to give appropriate assumptions about the weight function a (x) for studying our problem. Based on this, we first obtain the existence of a bounded absorbing set, then verify the asymptotic compactness of a solution semigroup via the asymptotic contractive semigroup method. Finally, the existence and uniqueness of global attractors are proved. In particular, the nonlinearity f satisfies the polynomial growth of arbitrary order p − 1 (p ≥ 2 ) and the idea of uniform tail-estimates of solutions is employed to show the strong convergence of solutions. [ABSTRACT FROM AUTHOR]