On quasilinear parabolic equations involving weighted \(p\)-Laplacian operators (Q969600)

The initial boundary value problem for a class of quasilinear parabolic equations involving weighted \(p\)-Laplacian operators in an arbitrary domain is considered. The conditions imposed on the nonlinearity provide global existence of solutions, but not uniqueness. The long-time behavior of the solutions to that problem is considered via the concept of global attractor for multivalued semiflows. In more precise terms, it is shown that the conditions imply the existence of a strict multivalued semiflow which possesses an invariant compact global attractor. The obtained results recover and extend some known results related to the \(p\)-Laplacian equations.