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

Considered here is the first initial boundary value problem for a semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain Ω . We prove the regularity and exponential growth of a pullback attractor in the space 𠑆 2 0 ( Ω ) ∩ ð ¿ 2 ð ‘ âˆ’ 2 ( Ω ) 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.