Electron. J. Diff. Equ., Vol. 2012 (2012), No. 207, pp. 1-22.

Regularity of random attractors for stochastic semilinear degenerate parabolic equations

Cung The Anh, Tang Quoc Bao, Nguyen Van Thanh

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.

Show me the PDF file (341 KB), TEX file, and other files for this article.

Cung The Anh
Department of Mathematics
Hanoi National Univiersity of Education
136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
email: anhctmath@hnue.edu.vn
Tang Quoc Bao
School of Applied Mathematics and Informatics
Hanoi University of Science and Technology
1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam
email: baotangquoc@gmail.com
Nguyen Van Thanh
Foreign Languages Specialized School
University Of Languages and International Studies
Hanoi National University
2 Pham Van Dong, Cau Giay, Hanoi, Vietnam
email: thanhnvmath@gmail.com

Return to the EJDE web page