Stability and Optimal Decay Rates for Abstract Systems with Thermal Damping of Cattaneo's Type
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917779996672000 |
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| author | Deng, Chenxi Han, Zhong-Jie Kuang, Zhaobin Zhang, Qiong |
| author_facet | Deng, Chenxi Han, Zhong-Jie Kuang, Zhaobin Zhang, Qiong |
| contents | This paper studies the stability of an abstract thermoelastic system with Cattaneo's law, which describes finite heat propagation speed in a medium. We introduce a region of parameters containing coupling, thermal dissipation, and possible inertial characteristics. The region is partitioned into distinct subregions based on the spectral properties of the generator of the corresponding semigroup. By a careful estimation of the resolvent operator on the imaginary axis, we obtain distinct polynomial decay rates for systems with parameters located in different subregions. Furthermore, the optimality of these decay rates is proved. Finally, we apply our results to several coupled systems of partial differential equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_00988 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability and Optimal Decay Rates for Abstract Systems with Thermal Damping of Cattaneo's Type Deng, Chenxi Han, Zhong-Jie Kuang, Zhaobin Zhang, Qiong Analysis of PDEs 35Q74(Primary) 74F05(Secondary) This paper studies the stability of an abstract thermoelastic system with Cattaneo's law, which describes finite heat propagation speed in a medium. We introduce a region of parameters containing coupling, thermal dissipation, and possible inertial characteristics. The region is partitioned into distinct subregions based on the spectral properties of the generator of the corresponding semigroup. By a careful estimation of the resolvent operator on the imaginary axis, we obtain distinct polynomial decay rates for systems with parameters located in different subregions. Furthermore, the optimality of these decay rates is proved. Finally, we apply our results to several coupled systems of partial differential equations. |
| title | Stability and Optimal Decay Rates for Abstract Systems with Thermal Damping of Cattaneo's Type |
| topic | Analysis of PDEs 35Q74(Primary) 74F05(Secondary) |
| url | https://arxiv.org/abs/2310.00988 |