Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 207, pp. 1-22.

Title: Regularity of random attractors for stochastic semilinear 
       degenerate parabolic equations
        
Authors: Cung The Anh (Hanoi National Univ. of Education, Vietnam)
         Tang Quoc Bao (Hanoi Univ. of Science and Tech., Vietnam}
	 Nguyen Van Thanh (Hanoi National Univ. , Vietnam)

Abstract:
 We consider the  stochastic semilinear degenerate parabolic equation
 $$
 du+[- \operatorname{div}(\sigma(x)\nabla u) + f(u) + \lambda u]dt
 = gdt+  \sum_{j=1}^{m}h_j{d\omega_j}
 $$
 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 $\{\mathcal{A}(\omega)\}_{\omega\in\Omega}$
 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.

Submitted September 27, 2012. Published November 25, 2012.
Math Subject Classifications: 35B41, 37H10, 35K65.
Key Words: Random dynamical systems; random attractors; regularity;
           stochastic degenerate parabolic equations; 
	   asymptotic a priori estimate method.