Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909618852069376 |
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| author | Huang, Xinchi Yamamoto, Masahiro |
| author_facet | Huang, Xinchi Yamamoto, Masahiro |
| contents | We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. For the case of time-dependent coefficients, it is difficult to give an explicit solution formula by the eigenfunction expansion method. In order to deal with the case of time-varying coefficients, we first show the unique existence and regularity of solution to a system of time-fractional ordinary differential equations. Then the unique existence of the weak solution to the time-fractional partial differential equation and improved regularity are derived by using the Galerkin method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_10448 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients Huang, Xinchi Yamamoto, Masahiro Analysis of PDEs We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. For the case of time-dependent coefficients, it is difficult to give an explicit solution formula by the eigenfunction expansion method. In order to deal with the case of time-varying coefficients, we first show the unique existence and regularity of solution to a system of time-fractional ordinary differential equations. Then the unique existence of the weak solution to the time-fractional partial differential equation and improved regularity are derived by using the Galerkin method. |
| title | Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2203.10448 |