Pullback attractors for nonautonomous and random parabolicequations on non-smooth domains

Jianhua Huang; Wenxian Shen

doi:10.3934/dcds.2009.24.855

Article Contents

2009, Volume 24, Issue 3: 855-882. Doi: 10.3934/dcds.2009.24.855

This issue Previous Article Critical periods of a periodic annulus linking to equilibria at infinity in a cubic system Next Article Co-existence of traveling waves for a model of microbial growth and competition in a flow reactor

Pullback attractors for nonautonomous and random parabolic equations on non-smooth domains

Jianhua Huang^1, and
Wenxian Shen^2,

1.
Department of Mathematics, National University of Defense Technology, Changsha, 410073
2.
Department of Mathematics, Auburn University, AL 36849-5310

Received: November 30, 2007

Revised: March 31, 2008

Published: August 2009

Abstract Related Papers Cited by

Abstract

The current paper is devoted to the study of pullback attractors for general nonautonomous and random parabolic equations on non-smooth domains $D$. Mild solutions are considered for such equations. We first extend various fundamental properties for solutions of smooth parabolic equations on smooth domains to solutions of general parabolic equations on non-smooth domains, including continuous dependence on parameters, monotonicity, and compactness, which are of great importance in their own. Under certain dissipative conditions on the nonlinear terms, we prove that mild solutions with initial conditions in $L_q(D)$ exist globally for $q$ » $1$. We then show that pullback attractors for nonautonomous and random parabolic equations on non-smooth domains exist in $L_q(D)$ for $1$ « $q$ < $\infty$.

Keywords:

Mathematics Subject Classification: 35B41, 35K55, 35R60, 37H10, 37L30, 37L55.

Citation:

Article Metrics

HTML views() PDF downloads(121) Cited by(0)

Pullback attractors for nonautonomous and random parabolic equations on non-smooth domains

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Pullback attractors for nonautonomous and random parabolic equations on non-smooth domains

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content