On quasilinear parabolic equations involving weighted p-Laplacian operators

Abstract

In this paper we consider the initial boundary value problem for a class of quasilinear parabolic equations involving weighted p-Laplacian operators in an arbitrary domain, in which the conditions imposed on the non-linearity provide the global existence, but not uniqueness of solutions. The long-time behavior of the solutions to that problem is considered via the concept of global attractor for multi-valued semiflows. The obtained results recover and extend some known results related to the p-Laplacian equations. © 2009 Birkhäuser Verlag Basel/Switzerland.