Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908430165344256 |
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| author | Meliani, Mostafa Said-Houari, Belkacem |
| author_facet | Meliani, Mostafa Said-Houari, Belkacem |
| contents | In nonlinear acoustics, higher-order-in-time equations arise when taking into account a class of thermal relaxation laws in the modeling of sound wave propagation. In the literature, these families of equations came to be known as Jordan--Moore--Gibson--Thompson (JMGT) models. In this work, we show the global existence of solutions relying only on minimal assumptions on the nonlocal damping kernel. In particular, our result covers the until-now open question of global existence of solutions for the fractionally damped JMGT model with quadratic gradient nonlinearity. The factional damping setting forces us to work with non-integrable kernels, which require a tailored approach in the analysis to control. This approach relies on exploiting the specific nonlinearity structure combined with a weak damping provided by the nonlocality kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation Meliani, Mostafa Said-Houari, Belkacem Analysis of PDEs 35L75, 35B25 In nonlinear acoustics, higher-order-in-time equations arise when taking into account a class of thermal relaxation laws in the modeling of sound wave propagation. In the literature, these families of equations came to be known as Jordan--Moore--Gibson--Thompson (JMGT) models. In this work, we show the global existence of solutions relying only on minimal assumptions on the nonlocal damping kernel. In particular, our result covers the until-now open question of global existence of solutions for the fractionally damped JMGT model with quadratic gradient nonlinearity. The factional damping setting forces us to work with non-integrable kernels, which require a tailored approach in the analysis to control. This approach relies on exploiting the specific nonlinearity structure combined with a weak damping provided by the nonlocality kernel. |
| title | Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation |
| topic | Analysis of PDEs 35L75, 35B25 |
| url | https://arxiv.org/abs/2507.01538 |