Global attractors for degenerate semilinear parabolic equations

Let ΩΩ be a smooth bounded domain in RN,(N≥2)RN,(N≥2). We consider the long-time behavior of solutions to the following problem {ut−div(σ(x)∇u)+f(u)=gin Ω×R+,u=0on ∂Ω×R+,u(x,0)=u0(x)in Ω, where u0,g∈L1(Ω)u0,g∈L1(Ω). The diffusion coefficient σ(x)σ(x) is measurable, nonnegative and is allowed to have a finite number of zeroes at some points. We provide the existence and uniqueness results for the problem. Then we establish some asymptotic regularity results on the solution and consider its long-time behavior. The existence of a global attractor is obtained in the proper space.