A backward problem for the time-fractional pseudo-parabolic equation with a variable coefficient
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912967016054784 |
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| author | Altybay, Arshyn |
| author_facet | Altybay, Arshyn |
| contents | This work addresses an inverse reconstruction task for a time-fractional pseudo-parabolic model with a temporally varying coefficient. By imposing Dirichlet boundary conditions, we aim to recover the unknown initial state from observations collected at the final time.
From a theoretical perspective, we derive existence and uniqueness results by proving that, under suitable hypotheses, the problem admits a unique solution. Computationally, we introduce a finite-difference discretisation based on a time-stepping strategy and provide a detailed stability and convergence analysis. Leveraging the resulting forward solver, we then formulate an initial-data identification procedure using Tikhonov regularisation. The proposed approach is validated with numerical simulations, and its resilience is assessed via experiments that incorporate perturbations in the final-time measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14223 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A backward problem for the time-fractional pseudo-parabolic equation with a variable coefficient Altybay, Arshyn Numerical Analysis 35R30, 35B45, 65M06, 65M32 This work addresses an inverse reconstruction task for a time-fractional pseudo-parabolic model with a temporally varying coefficient. By imposing Dirichlet boundary conditions, we aim to recover the unknown initial state from observations collected at the final time. From a theoretical perspective, we derive existence and uniqueness results by proving that, under suitable hypotheses, the problem admits a unique solution. Computationally, we introduce a finite-difference discretisation based on a time-stepping strategy and provide a detailed stability and convergence analysis. Leveraging the resulting forward solver, we then formulate an initial-data identification procedure using Tikhonov regularisation. The proposed approach is validated with numerical simulations, and its resilience is assessed via experiments that incorporate perturbations in the final-time measurements. |
| title | A backward problem for the time-fractional pseudo-parabolic equation with a variable coefficient |
| topic | Numerical Analysis 35R30, 35B45, 65M06, 65M32 |
| url | https://arxiv.org/abs/2603.14223 |