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.