An Inverse Almost Periodic Problem for a Semilinear Strongly Damped Wave Equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911590636322816 |
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| author | Kmit, Irina Protsakh, Nataliya Tkachenko, Viktor |
| author_facet | Kmit, Irina Protsakh, Nataliya Tkachenko, Viktor |
| contents | This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic functions. In addition to constructing a bounded strong solution, we determine a time-dependent source coefficient via an integral overdetermination condition ensuring well-posedness. After reducing the inverse problem to a direct one, we first establish existence and uniqueness of solutions to an associated problem on finite time intervals. We then extend these solutions to half-lines and construct a bounded strong solution on the whole real line as a limit of such extensions, and subsequently establish its uniqueness. In particular, periodic and almost periodic data yield periodic and almost periodic solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07081 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Inverse Almost Periodic Problem for a Semilinear Strongly Damped Wave Equation Kmit, Irina Protsakh, Nataliya Tkachenko, Viktor Analysis of PDEs 35B15, 35L71, 35R30 This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic functions. In addition to constructing a bounded strong solution, we determine a time-dependent source coefficient via an integral overdetermination condition ensuring well-posedness. After reducing the inverse problem to a direct one, we first establish existence and uniqueness of solutions to an associated problem on finite time intervals. We then extend these solutions to half-lines and construct a bounded strong solution on the whole real line as a limit of such extensions, and subsequently establish its uniqueness. In particular, periodic and almost periodic data yield periodic and almost periodic solutions. |
| title | An Inverse Almost Periodic Problem for a Semilinear Strongly Damped Wave Equation |
| topic | Analysis of PDEs 35B15, 35L71, 35R30 |
| url | https://arxiv.org/abs/2601.07081 |