Thermoelastic plates with type I heat conduction with second gradient
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912753243914240 |
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| author | Rivera, Jaime Muñoz Ochoa, Elena Ochoa Quintanilla, Ramón |
| author_facet | Rivera, Jaime Muñoz Ochoa, Elena Ochoa Quintanilla, Ramón |
| contents | This paper investigates the qualitative properties of thermoelastic plates modeled by the second-gradient theory with a Type I heat equation. We establish the exponential stability of the solutions. Our main contribution is to prove that the semigroup is non-differentiable when the bi-Laplacian operator appears in the heat equation. Additionally, we analyze the case where the elastic parameter is negative, demonstrating the uniqueness and instability of the solutions. Finally, in the one-dimensional quasi-static case, we demonstrate the existence and exponential decay of the solutions under specific conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermoelastic plates with type I heat conduction with second gradient Rivera, Jaime Muñoz Ochoa, Elena Ochoa Quintanilla, Ramón Analysis of PDEs 35B40, 74K20, 74F05, 35Q74 G.1.8 This paper investigates the qualitative properties of thermoelastic plates modeled by the second-gradient theory with a Type I heat equation. We establish the exponential stability of the solutions. Our main contribution is to prove that the semigroup is non-differentiable when the bi-Laplacian operator appears in the heat equation. Additionally, we analyze the case where the elastic parameter is negative, demonstrating the uniqueness and instability of the solutions. Finally, in the one-dimensional quasi-static case, we demonstrate the existence and exponential decay of the solutions under specific conditions. |
| title | Thermoelastic plates with type I heat conduction with second gradient |
| topic | Analysis of PDEs 35B40, 74K20, 74F05, 35Q74 G.1.8 |
| url | https://arxiv.org/abs/2512.06625 |