On the dynamics of nonautonomous parabolic systems involving the Grushin operators (Q539346)

Summary: 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 \({\mathcal D}\)-attractor in \((L^2 (\Omega))^m\) for the corresponding process in the general case. When the system has a special gradient structure, we prove that the obtained pullback \({\mathcal D}\)-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.