Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data

Abstract

ABSTRACT This paper focuses on the following degenerate parabolic equation where Ω is a smooth bounded domain in , is positive almost everywhere and satisfies proper degenerate conditions. The existence and uniqueness result is proved in the framework of entropy solutions. For the long-time behavior, we prove the existence of a global attractor in by using some delicate estimates on the solution, which are derived by taking advantage of both the leading operator and the zero-order nonlinear term. The aforementioned results improve some previous results in the literature in several aspects.