## Topological Methods in Nonlinear Analysis

### On the asymptotic behavior of strongly damped wave equations

#### Abstract

This paper is devoted to the asymptotic behavior of the semi-linear strongly damped wave equation with forcing term only belongs to $H^{-1}$. Some refined decompositions of the solution have been presented, which allow to remove the quasi-monotone condition $f'(s)> -k$. The asymptotic regularity and existence of a finite-dimensional exponential attractor are established under the usual assumptions.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 44, Number 1 (2014), 161-175.

Dates
First available in Project Euclid: 11 April 2016

https://projecteuclid.org/euclid.tmna/1460381475

Mathematical Reviews number (MathSciNet)
MR3289013

Zentralblatt MATH identifier
1368.35186

#### Citation

Du, Yunlong; Li, Xin; Sun, Chunyou. On the asymptotic behavior of strongly damped wave equations. Topol. Methods Nonlinear Anal. 44 (2014), no. 1, 161--175. https://projecteuclid.org/euclid.tmna/1460381475

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