Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator

Abstract

Considered here is the first initial boundary value problem for a semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain $\Omega$. We prove the regularity and exponential growth of a pullback attractor in the space $S_0^2\left(\Omega \right)\cap L^{2p-2}\left(\Omega \right)$ for the nonautonomous dynamical system associated to the problem. The obtained results seem to be optimal and, in particular, improve and extend some recent results on pullback attractors for reaction-diffusion equations in bounded domains.