Differential and Integral Equations

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

Ryo Ikehata and Michiaki Onodera

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1493863392

Mathematical Reviews number (MathSciNet)
MR3646461

Zentralblatt MATH identifier
06738559

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35L15: Initial value problems for second-order hyperbolic equations 35L05: Wave equation 35C20: Asymptotic expansions

Citation

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


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