Multiple equilibrium points in global attractor for the weakly damped wave equation with critical exponent

Fengjuan Meng; Chengkui Zhong

doi:10.3934/dcdsb.2014.19.217

Article Contents

2014, Volume 19, Issue 1: 217-230. Doi: 10.3934/dcdsb.2014.19.217

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Multiple equilibrium points in global attractor for the weakly damped wave equation with critical exponent

Fengjuan Meng^1, and
Chengkui Zhong^2,

1.
Department of Mathematics, Nanjing University, Nanjing, 210093
2.
Department of Mathematics, Nanjing University, Nanjing 210093

Received: October 31, 2012

Revised: May 31, 2013

Published: December 2013

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Abstract

In this paper, we are concerned with some properties of the global attractor of weakly damped wave equations. We get the existence of multiple stationary solutions for wave equations with weakly damping. Furthermore, we provide some approaches to verify the small neighborhood of the origin is an attracting domain which is important to obtain the multiple equilibrium points in global attractor.

Keywords:

Mathematics Subject Classification: Primary: 35L05, 37L05, 35B40; Secondary: 35B41, 58J20.

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