Regularity of random attractors for stochastic semilinear degenerate parabolic equations

• Main Authors: Cung The Anh, Tang Quoc Bao, Nguyen Van Thanh
• Format: Article
• Language: English
• Published: Texas State University 2012-11-01
• Series: Electronic Journal of Differential Equations
• Subjects: Random dynamical systems; random attractors; regularity; stochastic degenerate parabolic equations; asymptotic a priori estimate method
• Online Access: http://ejde.math.txstate.edu/Volumes/2012/207/abstr.html

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.