Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916080420651008 |
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| author | Benabbas, Imen Said-Houari, Belkacem |
| author_facet | Benabbas, Imen Said-Houari, Belkacem |
| contents | In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on the Jordan-Moore-Gibson-Thompson equation (JMGT) with temperature-dependent medium parameters coupled to the semilinear Pennes equation for the bioheat transfer. The equations are coupled via the temperature in the coefficients of the JMGT equation and via a nonlinear source term within the Pennes equation, which models the absorption of acoustic energy by the surrounding tissue. Using the energy method together with a fixed point argument, we prove that our model is locally well-posed, provided that the initial data are regular, small in a lower topology and the final time is short enough. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01709 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating Benabbas, Imen Said-Houari, Belkacem Analysis of PDEs In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on the Jordan-Moore-Gibson-Thompson equation (JMGT) with temperature-dependent medium parameters coupled to the semilinear Pennes equation for the bioheat transfer. The equations are coupled via the temperature in the coefficients of the JMGT equation and via a nonlinear source term within the Pennes equation, which models the absorption of acoustic energy by the surrounding tissue. Using the energy method together with a fixed point argument, we prove that our model is locally well-posed, provided that the initial data are regular, small in a lower topology and the final time is short enough. |
| title | Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.01709 |