On the Dynamics of Nonautonomous Parabolic Systems Involving the Grushin Operators

Abstract EN

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.