## Topological Methods in Nonlinear Analysis

### Pullback attractors for a non-autonomous semilinear degenerate parabolic equation

#### Abstract

In this paper, we consider the pullback attractors for a non-autonomous semilinear degenerate parabolic equation $u_{t}-{\rm div}(\sigma(x)\nabla u)+ f(u)=g(x,t)$ defined on a bounded domain $\Omega\subset \mathbb{R}^N$ with smooth boundary. We provide that the usual $(L^{2}(\Omega), L^{2}(\Omega))$ pullback $\mathscr{D}_{\lambda}$-attractor indeed can attract the $\mathscr{D}_{\lambda}$-class in $L^{2+\delta}(\Omega)$, where $\delta \in [0, \infty)$ can be arbitrary.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 47, Number 2 (2016), 511-528.

Dates
First available in Project Euclid: 13 July 2016

https://projecteuclid.org/euclid.tmna/1468413750

Digital Object Identifier
doi:10.12775/TMNA.2016.011

Mathematical Reviews number (MathSciNet)
MR3559918

Zentralblatt MATH identifier
1368.35162

#### Citation

Li, Xin; Sun, Chunyou; Zhou, Feng. Pullback attractors for a non-autonomous semilinear degenerate parabolic equation. Topol. Methods Nonlinear Anal. 47 (2016), no. 2, 511--528. doi:10.12775/TMNA.2016.011. https://projecteuclid.org/euclid.tmna/1468413750

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