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arXiv · 2512.06625

Thermoelastic plates with type I heat conduction with second gradient

Jaime Muñoz Rivera·Elena Ochoa Ochoa·Ramón Quintanilla
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Abstract

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.

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Jaime Muñoz Rivera, Elena Ochoa Ochoa, Ramón Quintanilla. 2025-12-07. Thermoelastic plates with type I heat conduction with second gradient. https://doi.org/10.58997/ejde.2025.94

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