## Differential and Integral Equations

### Remarks on large time behavior of the $L^{2}$-norm of solutions to strongly damped wave equations

#### Abstract

We reconsider the asymptotic behavior as $t \to +\infty$ of the $L^{2}$-norm of solutions to strongly damped wave equations in ${\bf R}^{n}$ with weighted initial data in the $n=1,2$ dimensional case. As an application, we shall apply those results to the analysis of the linearized compressible Navier-Stokes equations in ${\bf R}^{3}$.

#### Article information

Source
Differential Integral Equations, Volume 30, Number 7/8 (2017), 505-520.

Dates
Accepted: December 2016
First available in Project Euclid: 4 May 2017

Ikehata, Ryo; Onodera, Michiaki. Remarks on large time behavior of the $L^{2}$-norm of solutions to strongly damped wave equations. Differential Integral Equations 30 (2017), no. 7/8, 505--520. https://projecteuclid.org/euclid.die/1493863392