On the Jordan-Moore-Gibson-Thompson equation of nonlinear acoustics
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917389318225920 |
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| author | Kaltenbacher, Barbara |
| author_facet | Kaltenbacher, Barbara |
| contents | The JMGT equation was put forward by Pedro Jordan~\cite{jordan2008nonlinear,jordan2014second}, also referring to earlier work by Moore and Gibson~\cite{moore1960propagation}, as well as Thompson~\cite{thompson} to amend the infinite speed of sound paradox of classical models of nonlinear acoustics such as the Westervelt and Kuznetsov's equation. Additionally to its physical significance (and of course related to it), it has given rise to a substantial body of mathematical literature -- possibly even more than the above mentioned classical models. In this paper, we aim to provide a systematic (though inevitably incomplete) overview %and indicate some potential open questions. thereby focusing on well-posedness analysis of initial value and time periodic problems, memory and fractional attenuation as well as singular limits and -- with one example each -- control and inverse problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Jordan-Moore-Gibson-Thompson equation of nonlinear acoustics Kaltenbacher, Barbara Analysis of PDEs The JMGT equation was put forward by Pedro Jordan~\cite{jordan2008nonlinear,jordan2014second}, also referring to earlier work by Moore and Gibson~\cite{moore1960propagation}, as well as Thompson~\cite{thompson} to amend the infinite speed of sound paradox of classical models of nonlinear acoustics such as the Westervelt and Kuznetsov's equation. Additionally to its physical significance (and of course related to it), it has given rise to a substantial body of mathematical literature -- possibly even more than the above mentioned classical models. In this paper, we aim to provide a systematic (though inevitably incomplete) overview %and indicate some potential open questions. thereby focusing on well-posedness analysis of initial value and time periodic problems, memory and fractional attenuation as well as singular limits and -- with one example each -- control and inverse problems. |
| title | On the Jordan-Moore-Gibson-Thompson equation of nonlinear acoustics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.06340 |