Attractors for Nonautonomous Parabolic Equations without Uniqueness

Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connectedness of the uniform global attractor

Pullback attractors for non-autonomous parabolic equations involving Grushin operators

Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusion equations

Existence and continuity of global attractors for a degenerate semilinear parabolic equation

In this article, we study the existence and the upper semicontinuity with respect to the nonlinearity and the shape of the domain of global attractors for a semilinear degenerate parabolic equation involving the Grushin operator

On a Semilinear Strongly Degenerate Parabolic Equation in an Unbounded Domain

We study the existence and long-time behavior of solutions to a semilinear strongly degenerate parabolic equation on RN under an arbitrary polynomial growth order of the nonlinearity. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of global attractors is proved by combining the tail estimates method and the asymptotic a priori estimate method

On the Dynamics of Nonautonomous Parabolic Systems Involving the Grushin Operators

We study the long-time behavior of solutions to nonautonomous semilinear parabolic systems involving the Grushin operators in bounded domains. We prove the existence of a pullback D-attractor in (L2(Ω))m for the corresponding process in the general case. When the system has a special gradient structure, we prove that the obtained pullback D-attractor is more regular and has a finite fractal dimension. The obtained results, in particular, extend and improve some existing ones for the reaction-diffusion equations and the Grushin equations