Global attractors for degenerate semilinear parabolic equations

摘要

Let Ω be a smooth bounded domain in R ~N,(N<2). We consider the long-time behavior of solutions to the following problem u _t-div(σ(x)?u)+f(u)=gin Ω× ~(R+),u=0on ?Ω× ~(R+),u(x,0)=u 0(x)in Ω, where u _0,g∈L _(1)(Ω). The diffusion coefficient 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.