Global attractors for degenerate semilinear parabolic equations

Let Omega 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(sigma(x)del u) + f(u) = g in Omega x R+ {u = 0 on partial derivative Omega x R+, {u(x, 0) = u(0)(x) in Omega, where u(0), g is an element of L-1(Omega). The diffusion coefficient sigma(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. (C) 2012 Elsevier Ltd. All rights reserved.