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Research Article | Open Access

Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space

Yusuke Ishigaki1, Yoshihiro Ueda2( )
Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka-shi Osaka 560-8531, Japan
Faculty of Maritime Sciences, Kobe University, Kobe 658-0022, Japan
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Abstract

The system of equations describing motion of compressible viscoelastic fluids is considered in a one dimensional half space under the outflow boundary condition. We investigate the existence and stability of stationary solutions. It is shown that the stationary solution exists for large Mach number and small number of propagation speed of elastic wave. We next show that the stationary solution is asymptotically stable, provided that the initial perturbation is sufficiently small.

Keywords

compressible viscoelastic systemenergy methodoutflow problemstationary solutionasymptotic stability
CLC number: 35Q35, 35B40, 76N10

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 33215-33253
DOI: 10.3934/math.20241585

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Cite this article:
Ishigaki Y, Ueda Y. Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space. AIMS Mathematics, 2024, 9(11): 33215-33253. https://doi.org/10.3934/math.20241585

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Received: 24 September 2024
Revised: 06 November 2024
Accepted: 06 November 2024
Published: 21 November 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)