Well-posedness and global extensibility criteria for time-fractionally damped Jordan--Moore--Gibson--Thompson equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929555385614336 |
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| author | Meliani, Mostafa Said-Houari, Belkacem |
| author_facet | Meliani, Mostafa Said-Houari, Belkacem |
| contents | In this paper, we consider the Jordan--Moore--Gibson--Thompson with a time-fractional damping term of the type $δ\textup{D}_t^{1-α} Δ\psit$ where we allow the challenging so-called critical case ($δ=0$). This equation arises in the context of acoustic propagation through thermally relaxed media. We tackle the question of long-time existence of the solution. More precisely, the goal of the paper is twofold: First, we establish local well-posedness of the initial boundary value problem, where we also provide a lower bound on the final time of existence as a function of initial data. Second, we prove a regularity result which guarantees, under the hypothesis of boundedness of certain quantities, that the local solution can be extended to be global-in-time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness and global extensibility criteria for time-fractionally damped Jordan--Moore--Gibson--Thompson equation Meliani, Mostafa Said-Houari, Belkacem Analysis of PDEs In this paper, we consider the Jordan--Moore--Gibson--Thompson with a time-fractional damping term of the type $δ\textup{D}_t^{1-α} Δ\psit$ where we allow the challenging so-called critical case ($δ=0$). This equation arises in the context of acoustic propagation through thermally relaxed media. We tackle the question of long-time existence of the solution. More precisely, the goal of the paper is twofold: First, we establish local well-posedness of the initial boundary value problem, where we also provide a lower bound on the final time of existence as a function of initial data. Second, we prove a regularity result which guarantees, under the hypothesis of boundedness of certain quantities, that the local solution can be extended to be global-in-time. |
| title | Well-posedness and global extensibility criteria for time-fractionally damped Jordan--Moore--Gibson--Thompson equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.17826 |