On uniform global attractors for a class of non-autonomous degenerate parabolic equations

Abstract

Using the theory of Multivalued Semiprocesses (MSPs) of Melnik and Valero, we prove the existence of a uniform global attractor for a non-autonomous quasilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. In the semilinear case, we prove the Kneser property holds for solutions, and as a result we obtain the connectedness of the uniform global attractor. We also study the regularity of the uniform attractor in this case under some additional restrictions of the nonlinearity and the external force.