Regularity and exponential growth of pullback attractors for semilinear parabolic equations involving the Grushin operator (Q417118)

Summary: 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 \(S^2_0(\Omega) \cap L^{2p-2}(\Omega)\) 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.