Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data.

This paper focuses on the following degenerate parabolic equation u t − d i v (σ (x) | ∇ u | p − 2 ∇ u) + f (x , u) = g i n Ω × R + , u = 0 o n ∂ Ω × R + , u (x , 0) = u 0 (x) i n Ω , where Ω is a smooth bounded domain in R N , (N ≥ 2) , 1 < p < N , u 0 , g ∈ L 1 (Ω) , σ (x) 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 L q (Ω) 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. [ABSTRACT FROM AUTHOR]