Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space
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...
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241585?viewType=HTML |
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| _version_ | 1846140964217815040 |
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| author | Yusuke Ishigaki Yoshihiro Ueda |
| author_facet | Yusuke Ishigaki Yoshihiro Ueda |
| author_sort | Yusuke Ishigaki |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-19a8c804679f4a2e9164133c5b113e29 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-19a8c804679f4a2e9164133c5b113e292024-12-05T01:18:04ZengAIMS PressAIMS Mathematics2473-69882024-11-01911332153325310.3934/math.20241585Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half spaceYusuke Ishigaki0Yoshihiro Ueda11. Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka-shi Osaka 560-8531, Japan2. Faculty of Maritime Sciences, Kobe University, Kobe 658-0022, JapanThe 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.https://www.aimspress.com/article/doi/10.3934/math.20241585?viewType=HTMLcompressible viscoelastic systemenergy methodoutflow problemstationary solutionasymptotic stability |
| spellingShingle | Yusuke Ishigaki Yoshihiro Ueda Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space AIMS Mathematics compressible viscoelastic system energy method outflow problem stationary solution asymptotic stability |
| title | Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space |
| title_full | Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space |
| title_fullStr | Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space |
| title_full_unstemmed | Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space |
| title_short | Stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space |
| title_sort | stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space |
| topic | compressible viscoelastic system energy method outflow problem stationary solution asymptotic stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241585?viewType=HTML |
| work_keys_str_mv | AT yusukeishigaki stabilityofstationarysolutionstooutflowproblemforcompressibleviscoelasticsysteminonedimensionalhalfspace AT yoshihiroueda stabilityofstationarysolutionstooutflowproblemforcompressibleviscoelasticsysteminonedimensionalhalfspace |