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

Messaoudi, Salim A.; Mustafa, Muhammad I.

doi:10.1002/mma.1047

Cited by 62 publications

(24 citation statements)

References 13 publications

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“…Whereas, in the opposite case

\frac{κ}{ρ_{1}} \neq \frac{b}{ρ_{2}}

, a weaker rate of decay is obtained for strong solutions. In this regard, we quote, among others, the work of Soufyane and Wehbe , Guesmia and Messaoudi Rivera and Fernández Sare , Rivera and Racke , Messaoudi and Mustafa , and Messaoudi and Said‐Houari . Similar results were obtained by Almeida Júnior et al , when the damping term is in the first equation.…”

Section: Introductionsupporting

confidence: 80%

On the decay rates of Timoshenko system with second sound

Apalara

Messaoudi

Keddi

2015

Math Methods in App Sciences

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In this work, we study the well‐posedness and the asymptotic stability of a one‐dimensional linear thermoelastic Timoshenko system, where the heat conduction is given by Cattaneo's law and the coupling is via the displacement equation. We prove that the system is exponentially stable provided that the stability number χτ=0. Otherwise, we show that the system lacks exponential stability. Furthermore, in the latter case, we show that the solution decays polynomially. Copyright © 2015 John Wiley & Sons, Ltd.

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“…Whereas, in the opposite case

\frac{κ}{ρ_{1}} \neq \frac{b}{ρ_{2}}

Section: Introductionsupporting

confidence: 80%

On the decay rates of Timoshenko system with second sound

Apalara

Messaoudi

Keddi

2015

Math Methods in App Sciences

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“…For more results concerning well-posedness and controllability of Timoshenko systems, we refer the reader to Alabau-Boussouira [1], Fernández Sare and Racke [6], and Messaoudi and Mustafa [12].…”

Section: Introductionmentioning

confidence: 99%

Uniform decay in a Timoshenko-type system with past history

Messaoudi

Said‐Houari

2009

Journal of Mathematical Analysis and Applications

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of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482-502] considered the following Timoshenko-type systemwhere g is a positive differentiable exponentially decaying function. They established an exponential decay result in the case of equal wave-speed propagation and a polynomial decay result in the case of nonequal wave-speed propagation. In this paper, we study the same system, for g decaying polynomially, and prove polynomial stability results for the equal and nonequal wave-speed propagation. Our results are established under conditions on the relaxation function weaker than those in [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482-502].

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“…He also obtained the rate of decay of the energy, which is exactly the rate of decay of the relaxation functions. This last result has been improved and generalized by Messaoudi and Soufyane [13] and Messaoudi and Mustafa [15] (see also [17][18][19]22,26]). …”

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confidence: 68%