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

Yusuke Ishigaki; Yoshihiro Ueda; Yusuke Ishigaki; Yoshihiro Ueda

doi:10.3934/math.20241585

AIMS Mathematics

2024, Volume 9, Issue 11: 33215-33253. doi: 10.3934/math.20241585

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Research article

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

Yusuke Ishigaki ¹,
Yoshihiro Ueda ^{2
,
,}

1.
Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka-shi Osaka 560-8531, Japan
2.
Faculty of Maritime Sciences, Kobe University, Kobe 658-0022, Japan

Received: 24 September 2024 Revised: 06 November 2024 Accepted: 06 November 2024 Published: 21 November 2024
MSC : 35Q35, 35B40, 76N10

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.
- compressible viscoelastic system,
- energy method,
- outflow problem,
- stationary solution,
- asymptotic stability
Citation: Yusuke Ishigaki, Yoshihiro Ueda. Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space[J]. AIMS Mathematics, 2024, 9(11): 33215-33253. doi: 10.3934/math.20241585

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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.

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