Regularity of random attractors for stochastic semilinear degenerate parabolic equations

Abstract

We consider the stochastic semilinear degenerate parabolic equation $$ du+[- operatorname{div}(sigma(x)abla u) + f(u) + lambda u]dt = gdt+ sum_{j=1}^{m}h_j{domega_j} $$ in a bounded domain $mathcal{O}subset mathbb {R}^N$, with the nonlinearity satisfies an arbitrary polynomial growth condition. The random dynamical system generated by the equation is shown to have a random attractor ${mathcal{A}(omega)}_{omegainOmega}$ in $mathcal D_0^1(mathcal{O},sigma)cap L^p(mathcal{O})$. The results obtained improve some recent ones for stochastic semilinear degenerate parabolic equations.

Keywords

• Random dynamical systems
• random attractors
• regularity
• stochastic degenerate parabolic equations
• asymptotic a priori estimate method