Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems

This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Júnior et al. (Z Angew Math Phys 65(6):1233–1249, 2014 ) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates dependin...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2016-06, Vol.67 (3), p.1-16, Article 70
Main Authors: Alves, M. S., Jorge Silva, M. A., Ma, T. F., Muñoz Rivera, J. E.
Format: Article
Language:English
Subjects:
Applications of mathematics
Boundary conditions
Decay rate
Dirichlet problem
Engineering
Invariance
Mathematical Methods in Physics
Optimization
Polynomials
Stability
Theoretical and Applied Mechanics
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Summary:This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Júnior et al. (Z Angew Math Phys 65(6):1233–1249, 2014 ) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates depending on the boundary conditions, namely, optimal rate t - 1 / 2 for mixed Dirichlet–Neumann boundary condition and rate t - 1 / 4 for full Dirichlet boundary condition. Here, our main achievement is to prove the same polynomial decay rate t - 1 / 2 (corresponding to the optimal one) independently of the boundary conditions, which improves the existing literature on the subject. As a complementary result, we also prove that the system is exponentially stable under equal wave speeds assumption. The technique employed here can probably be applied to other kind of thermoelastic systems.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-016-0662-y