Well-posedness of the initial boundary value problem for degenerate hyperbolic systems with a localized term and its application to the linearized system for the motion of an inextensible hanging string
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917069849624576 |
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| author | Iguchi, Tatsuo Takayama, Masahiro |
| author_facet | Iguchi, Tatsuo Takayama, Masahiro |
| contents | Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems with a localized term and show its well-posedness in weighted Sobolev spaces. We then consider the linearized system for the motion of an inextensible hanging string. Well-posedness of its initial boundary value problem is demonstrated as an application of the result obtained in the first part. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the initial boundary value problem for degenerate hyperbolic systems with a localized term and its application to the linearized system for the motion of an inextensible hanging string Iguchi, Tatsuo Takayama, Masahiro Analysis of PDEs Primary: 35L53, Secondary: 35L80, 74K05 Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems with a localized term and show its well-posedness in weighted Sobolev spaces. We then consider the linearized system for the motion of an inextensible hanging string. Well-posedness of its initial boundary value problem is demonstrated as an application of the result obtained in the first part. |
| title | Well-posedness of the initial boundary value problem for degenerate hyperbolic systems with a localized term and its application to the linearized system for the motion of an inextensible hanging string |
| topic | Analysis of PDEs Primary: 35L53, Secondary: 35L80, 74K05 |
| url | https://arxiv.org/abs/2404.05292 |