Pullback attractors for nonautonomous and random parabolicequations on non-smooth domains

The current paper is devoted to the study of pullback attractors forgeneral nonautonomous and random parabolic equations on non-smoothdomains D. Mild solutions are considered for such equations. Wefirst extend various fundamental properties for solutions of smoothparabolic equations on smooth domains to solutions of generalparabolic equations on non-smooth domains, including continuousdependence on parameters, monotonicity, and compactness, which areof great importance in their own. Under certain dissipativeconditions on the nonlinear terms, we prove that mild solutionswith initial conditions in Lq(D) exist globally for q » $1$. Wethen show that pullback attractors for nonautonomous and randomparabolic equations on non-smooth domains exist in Lq(D) for$1$ « q < ∞.