Exponential stability for the Timoshenko system with two weak dampings

Raposo, Carlos A.; Ferreira, J.; Santos, Mauro de Lima; Castro, Nelson Nery de Oliveira

doi:10.1016/j.aml.2004.03.017

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Cited by 178 publications

(84 citation statements)

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“…This last result has been improved and generalized by Messaoudi and Soufyane [7]. Raposo et al [8] treated the following system:…”

Section: Introductionmentioning

confidence: 84%

On the stabilization of the Timoshenko system by a weak nonlinear dissipation

Messaoudi

Mustafa

2008

Math Methods in App Sciences

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“…This last result has been improved and generalized by Messaoudi and Soufyane [7]. Raposo et al [8] treated the following system:…”

Section: Introductionmentioning

confidence: 84%

On the stabilization of the Timoshenko system by a weak nonlinear dissipation

Messaoudi

Mustafa

2008

Math Methods in App Sciences

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“…For the case of nonlinear internal frictional damping and without thermal effects, we refer the readers to Boussouira [1], Rivera and Racke [35], Raposo et al [40] and Soufyane [43]. The boundary stabilization and boundary control have been studied in [25,46] (see also references therein).…”

Section: Introductionmentioning

confidence: 99%

Global Existence and Exponential Decay for a Dynamic Contact Problem of Thermoelastic Timoshenko Beam with Second Sound

Liu¹,

Chen²,

Zhu³

2017

Preprint

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In this paper, we study the global existence and exponential decay for a dynamic contact problem between a Timoshenko beam with second sound and two rigid obstacles, of which the heat flux is given by Cattaneo's law instead of the usual Fourier's law.The main difficulties arise from the irregular boundary terms, from the low regularity of the weak solution and from the weaker dissipative effects of heat conduction induced by Cattaneo's law. By considering related penalized problems, proving some a priori estimates and passing to the limit, we prove the global existence of the solutions.By considering the approximate framework, constructing some new functionals and applying the perturbed energy method, we obtain the exponential decay result for the approximate solution, and then prove the exponential decay rate to the original problem by utilizing the weak lower semicontinuity arguments.

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“…There are a number of publications concerning the stabilization of Timoshenko system with different kinds of damping (see [2], [3], [4] and [5]). Raposo et al [6] proved the exponential decay of the solution for the following linear system of Timoshenko-type beam equations with linear frictional dissipative terms:…”

Section: Introductionmentioning

confidence: 99%