An Inverse Source Problem For a Time-Fractional Mixed Wave-Diffusion-Wave Equation in a Cylindrical Domain
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915978268377088 |
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| author | Karimov, Erkinjon Toshpulatov, Muzaffar |
| author_facet | Karimov, Erkinjon Toshpulatov, Muzaffar |
| contents | This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the model to effectively capture temporal transitions between wave-like and diffusive behaviors. The solution is constructed in the form of a Fourier-Bessel series. By employing the method of separation of variables together with fundamental properties of Bessel functions, we analyze the uniform convergence of the resulting infinite series. This analysis ultimately leads to a rigorous proof of the existence of a solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02779 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Inverse Source Problem For a Time-Fractional Mixed Wave-Diffusion-Wave Equation in a Cylindrical Domain Karimov, Erkinjon Toshpulatov, Muzaffar Analysis of PDEs 35M10, 35R11 This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the model to effectively capture temporal transitions between wave-like and diffusive behaviors. The solution is constructed in the form of a Fourier-Bessel series. By employing the method of separation of variables together with fundamental properties of Bessel functions, we analyze the uniform convergence of the resulting infinite series. This analysis ultimately leads to a rigorous proof of the existence of a solution. |
| title | An Inverse Source Problem For a Time-Fractional Mixed Wave-Diffusion-Wave Equation in a Cylindrical Domain |
| topic | Analysis of PDEs 35M10, 35R11 |
| url | https://arxiv.org/abs/2605.02779 |