Inverse problem for wave equation of memory type with acoustic boundary conditions: Global solvability
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917284609523712 |
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| author | Totieva, Zhanna D. Kinra, Kush Mohan, Manil T. |
| author_facet | Totieva, Zhanna D. Kinra, Kush Mohan, Manil T. |
| contents | In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A wave equation with initial and acoustic boundary conditions in media with dispersion is used as a mathematical model. The inverse problem is reduced to an equivalent problem with homogeneous boundary conditions for the system of integro-differential equations. Using the technique of estimating integral equations and the contraction mappings principle in Sobolev spaces, the global existence and uniqueness theorem for the inverse problem is proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse problem for wave equation of memory type with acoustic boundary conditions: Global solvability Totieva, Zhanna D. Kinra, Kush Mohan, Manil T. Analysis of PDEs Mathematical Physics 35R30, 35L05, 35L20, 35Q99 In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A wave equation with initial and acoustic boundary conditions in media with dispersion is used as a mathematical model. The inverse problem is reduced to an equivalent problem with homogeneous boundary conditions for the system of integro-differential equations. Using the technique of estimating integral equations and the contraction mappings principle in Sobolev spaces, the global existence and uniqueness theorem for the inverse problem is proved. |
| title | Inverse problem for wave equation of memory type with acoustic boundary conditions: Global solvability |
| topic | Analysis of PDEs Mathematical Physics 35R30, 35L05, 35L20, 35Q99 |
| url | https://arxiv.org/abs/2505.07405 |