On the Dynamics of Nonautonomous Parabolic Systems Involving the Grushin Operators

Abstract

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 -attractor in for the corresponding process in the general case. When the system has a special gradient structure, we prove that the obtained pullback -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.