Uniform decay in a Timoshenko-type system with past history |
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| Authors: | Salim A Messaoudi Belkacem Said-Houari |
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| Institution: | aDepartment of Mathematics and Statistics, KFUPM, Dhahran 31261, Saudi Arabia;bInstitut de Mathématiques de Toulouse, MIP, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 09, France;cLaboratoire de Mathématiques Appliquées, Université Badji Mokhtar, B.P. 12, Annaba 23000, Algeria |
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| Abstract: | Fernández Sare and Rivera H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502] considered the following Timoshenko-type system | where 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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| Keywords: | Exponential decay Polynomial decay Timoshenko Past history Relaxation function |
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