A Mixed Problem for the Wave Equation in a Curvilinear Half-Strip with Discontinuous Initial Data
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914097652563968 |
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| author | Korzyuk, Viktor I. Rudzko, Jan V. Kolyachko, Vladislav V. |
| author_facet | Korzyuk, Viktor I. Rudzko, Jan V. Kolyachko, Vladislav V. |
| contents | For a one-dimensional wave equation, we consider a mixed problem in a curvilinear half-strip. The initial conditions have a first-kind discontinuity at one point. The mixed problem models the problem of a longitudinal impact on a finite elastic rod with a movable boundary. We construct the solution using the method of characteristics in an explicit analytical form. For the problem in question, we prove the uniqueness of the solution and establish the conditions under which its classical solution exists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Mixed Problem for the Wave Equation in a Curvilinear Half-Strip with Discontinuous Initial Data Korzyuk, Viktor I. Rudzko, Jan V. Kolyachko, Vladislav V. Analysis of PDEs 35A01, 35A02, 35A09, 35L20, 35L67, 35Q74, 35R37 For a one-dimensional wave equation, we consider a mixed problem in a curvilinear half-strip. The initial conditions have a first-kind discontinuity at one point. The mixed problem models the problem of a longitudinal impact on a finite elastic rod with a movable boundary. We construct the solution using the method of characteristics in an explicit analytical form. For the problem in question, we prove the uniqueness of the solution and establish the conditions under which its classical solution exists. |
| title | A Mixed Problem for the Wave Equation in a Curvilinear Half-Strip with Discontinuous Initial Data |
| topic | Analysis of PDEs 35A01, 35A02, 35A09, 35L20, 35L67, 35Q74, 35R37 |
| url | https://arxiv.org/abs/2507.08859 |