PreprintarXiv licencearXiv
Lack of exponential stability for thermoelastic Timoshenko and Bresse systems with full homogeneous Dirichlet boundary conditions
Abstract
In this paper we prove that the classical thermoelastic Timoshenko and Bresse systems with thermal coupling acting only on the bending moment are not exponentially stable under full homogeneous Dirichlet boundary conditions if the equal wave speed condition is not satisfied. Combined with their well-known converses, our results provide complete characterizations of exponential stability in terms of the coefficients of each system. To the best of our knowledge, these characterizations were previously known only under mixed boundary conditions. The proof is based on the introduction of a boundary correction term in the standard trigonometric ansatz so that the full homogeneous Dirichlet conditions are satisfied.
Related
- Carleman estimates for a nonconservative Timoshenko beam involving Dirichlet-Neumann boundary conditions and application to exact controllability
- Numerical Analysis for a Nonlinear Coupled Thermoelastic System with Acoustic Boundary Conditions
- Well-posedness and Stability of Thermoelastic Suspension Bridges with Cattaneo Heat Conduction: The Role of Viscoelastic Memory
- The Three-Dimensional Divergence-Curl Problem with Homogeneous Boundary Conditions and Pseudo-Harmonic Fields
- A doubly nonlinear parabolic problem with variable exponents, homogeneous Neumann boundary conditions and generalized logistic source
BibTeX
@misc{lima2026lack,
title = {{Lack of exponential stability for thermoelastic Timoshenko and Bresse systems with full homogeneous Dirichlet boundary conditions}},
author = {Pedro Roberto de Lima},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15890},
eprint = {2610.15890},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15890},
}
RIS
TY - UNPB
TI - Lack of exponential stability for thermoelastic Timoshenko and Bresse systems with full homogeneous Dirichlet boundary conditions
AU - Pedro Roberto de Lima
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15890
UR - https://arxiv.org/abs/2610.15890
AB - In this paper we prove that the classical thermoelastic Timoshenko and Bresse systems with thermal coupling acting only on the bending moment are not exponentially stable under full homogeneous Dirichlet boundary conditions if the equal wave speed condition is not satisfied. Combined with their well-known converses, our results provide complete characterizations of exponential stability in terms of the coefficients of each system. To the best of our knowledge, these characterizations were previously known only under mixed boundary conditions. The proof is based on the introduction of a boundary correction term in the standard trigonometric ansatz so that the full homogeneous Dirichlet conditions are satisfied.
ER -