Jaime Munoz Rivera, Elena Ochoa Ochoa, Ramon Quintanilla
Abstract:
This article studies 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.
Submitted September 28, 2025. Published October 9, 2025.
Math Subject Classifications: 74K20, 74F05, 74H20, 74H40.
Key Words: Euler Bernoulli equation; semigroup theory; smoothing effect.
DOI: 10.58997/ejde.2025.94
Show me the PDF file (355 KB), TEX file for this article.
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Jaime Muñoz Rivera Universidad del Bío-Bío Departamento de Matemática Facultad de Ciencias Avenida Collao 1202, Concepción, Chile email: jemunozrivera@gmail.com |
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Elena Ochoa Ochoa Universidad Andres Bello Departamento de Matemáticas Facultad de Ciencias Exactas Sede Concepción Autopista Concepción-Talcahuano 7100 Talcahuano, Chile email: elenaochoaochoa18@gmail.com |
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Ramón Quintanilla Universidad Politécnica de Catalunya Departamento de Matemáticas Colom 11, 08222 Terrassa, Spain email: ramon.quintanilla@upc.edu |
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