Large time asymptotic behavior for the weakly damped Jordan-Moore-Gibson-Thompson equation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914426504871936 |
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| author | Chen, Wenhui Liu, Yan Luo, Manqing |
| author_facet | Chen, Wenhui Liu, Yan Luo, Manqing |
| contents | This manuscript considers the Jordan-Moore-Gibson-Thompson (JMGT) equation and its linearized equation with an additional weak damping term (proposed by [B. Kaltenbacher, \emph{Inverse Problems} (2025)] firstly) in the whole space $\mathbb{R}^n$. We mainly study the unique existence and large time behavior, including optimal decay estimates and asymptotic profiles, of global in-time Sobolev solutions for any $n\geqslant 1$. This weak damping term leads to diffusion profiles in the sub-critical case $δ>0$ and regularity-loss decay properties in the critical case $δ=0$, which are greatly different from the results for the corresponding classical models without the weak damping term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26159 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large time asymptotic behavior for the weakly damped Jordan-Moore-Gibson-Thompson equation Chen, Wenhui Liu, Yan Luo, Manqing Analysis of PDEs This manuscript considers the Jordan-Moore-Gibson-Thompson (JMGT) equation and its linearized equation with an additional weak damping term (proposed by [B. Kaltenbacher, \emph{Inverse Problems} (2025)] firstly) in the whole space $\mathbb{R}^n$. We mainly study the unique existence and large time behavior, including optimal decay estimates and asymptotic profiles, of global in-time Sobolev solutions for any $n\geqslant 1$. This weak damping term leads to diffusion profiles in the sub-critical case $δ>0$ and regularity-loss decay properties in the critical case $δ=0$, which are greatly different from the results for the corresponding classical models without the weak damping term. |
| title | Large time asymptotic behavior for the weakly damped Jordan-Moore-Gibson-Thompson equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.26159 |