Singular Klein-Gordon equation on a bounded domain
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910801014554624 |
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| author | Ruzhansky, Michael Yeskermessuly, Alibek |
| author_facet | Ruzhansky, Michael Yeskermessuly, Alibek |
| contents | In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the existence, uniqueness and consistency of the very weak solution for the wave equation with singularities in the potential, initial data, source term, boundary and boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13460 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular Klein-Gordon equation on a bounded domain Ruzhansky, Michael Yeskermessuly, Alibek Analysis of PDEs 35L05, 35D30, 35L35, 35L81 In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the existence, uniqueness and consistency of the very weak solution for the wave equation with singularities in the potential, initial data, source term, boundary and boundary condition. |
| title | Singular Klein-Gordon equation on a bounded domain |
| topic | Analysis of PDEs 35L05, 35D30, 35L35, 35L81 |
| url | https://arxiv.org/abs/2501.13460 |