Well-posedness of the initial boundary value problem for the motion of an inextensible hanging string
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910842402897920 |
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| author | Iguchi, Tatsuo Takayama, Masahiro |
| author_facet | Iguchi, Tatsuo Takayama, Masahiro |
| contents | We consider the motion of an inextensible hanging string of finite length under the action of the gravity. The motion is governed by nonlinear and nonlocal hyperbolic equations, which is degenerate at the free end of the string. We show that the initial boundary value problem to the equations of motion is well-posed locally in time in weighted Sobolev spaces at the quasilinear regularity threshold under a stability condition. This paper is a continuation of our preceding articles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the initial boundary value problem for the motion of an inextensible hanging string Iguchi, Tatsuo Takayama, Masahiro Analysis of PDEs Primary: 74K05, Secondary: 35L20, 35L80 We consider the motion of an inextensible hanging string of finite length under the action of the gravity. The motion is governed by nonlinear and nonlocal hyperbolic equations, which is degenerate at the free end of the string. We show that the initial boundary value problem to the equations of motion is well-posed locally in time in weighted Sobolev spaces at the quasilinear regularity threshold under a stability condition. This paper is a continuation of our preceding articles. |
| title | Well-posedness of the initial boundary value problem for the motion of an inextensible hanging string |
| topic | Analysis of PDEs Primary: 74K05, Secondary: 35L20, 35L80 |
| url | https://arxiv.org/abs/2502.16904 |