Rothe's method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914335895322624 |
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| author | Van Bockstal, Karel Khompysh, Khonatbek Altybay, Arshyn |
| author_facet | Van Bockstal, Karel Khompysh, Khonatbek Altybay, Arshyn |
| contents | In this paper, we investigate the inverse problem of determining an unknown time-dependent source term in a semilinear pseudo-parabolic equation with variable coefficients and a Dirichlet boundary condition. The unknown source term is recovered from additional measurement data expressed as a weighted spatial average of the solution. By employing Rothe's time-discretisation method, we prove the existence and uniqueness of a weak solution under a smallness condition on the problem data. We also provide a numerical scheme based on a perturbation approach, which reduces the solution of the resulting discrete problem to solving two standard variational problems and evaluating a scalar coefficient, and we demonstrate its accuracy and stability through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rothe's method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation Van Bockstal, Karel Khompysh, Khonatbek Altybay, Arshyn Analysis of PDEs Numerical Analysis 35A01, 35A02, 35A15, 35R11, 65M12, 33E12 In this paper, we investigate the inverse problem of determining an unknown time-dependent source term in a semilinear pseudo-parabolic equation with variable coefficients and a Dirichlet boundary condition. The unknown source term is recovered from additional measurement data expressed as a weighted spatial average of the solution. By employing Rothe's time-discretisation method, we prove the existence and uniqueness of a weak solution under a smallness condition on the problem data. We also provide a numerical scheme based on a perturbation approach, which reduces the solution of the resulting discrete problem to solving two standard variational problems and evaluating a scalar coefficient, and we demonstrate its accuracy and stability through numerical experiments. |
| title | Rothe's method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation |
| topic | Analysis of PDEs Numerical Analysis 35A01, 35A02, 35A15, 35R11, 65M12, 33E12 |
| url | https://arxiv.org/abs/2510.20642 |