Institut Elie Cartan de Lorraine
UMR 7502, Université de Lorraine
3 Rue Augustin Fresnel, BP 45112
57073 Metz Cedex 03, France
email: aissa.guesmia@univ-lorraine.fr
Aissa Guesmia
Abstract:
In this article we study the decay of solutions for two systems of laminated Timoshenko
beams with interfacial slip, in the whole space R subject to a thermal effect
of type III acting only on one component.
When the thermal effect acts via the second or third component of the laminated
Timoshenko beam (rotation angle displacement or dynamic of the slip),
we prove that both systems are polynomially stable. Also we obtain stability estimates
in the L2(R)-norm of solutions and their higher order derivatives with respect
of the space variable. The decay rates, and the absence or presence of the
regularity-loss type property, depend on the regularity of the initial data and the speeds
of wave propagations. However, when the thermal effect acts via the first
component (transversal displacement), we introduce a new stability
number χ and prove that the stability of the system is equivalent to χ≠0.
An application to a case of lower order coupling terms is also given.
To prove our results, we use the energy method in the Fourier space combined with well
chosen weight functions to build appropriate Lyapunov functionals.
Submitted January 9, 2021. Published January 5, 2022.
Math Subject Classifications: 34B05, 34D05, 34H05.
Key Words: Timoshenko beam; interfacial slip; heat conduction; energy method; Fourier analysis.
DOI: https://doi.org/10.58997/ejde.2022.02
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Aissa Guesmia Institut Elie Cartan de Lorraine UMR 7502, Université de Lorraine 3 Rue Augustin Fresnel, BP 45112 57073 Metz Cedex 03, France email: aissa.guesmia@univ-lorraine.fr |
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