Global attractors for nonlinear parabolic equations with nonstandard growth and irregular data

We investigate the large time behavior of solutions to the following nonlinear parabolic equations{ut−div(|∇u|p(x)−2∇u)+f(x,u)=gin Ω×R+,u=0on ∂Ω×R+,u(x,0)=u0(x)in Ω, where u0,g∈L1(Ω). We first provide the existence and uniqueness of an entropy solution for the problem. Then through some delicate analysis, we establish some regularity results on the solution, by which we prove the existence of a global attractor for the solution semigroup.