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Tijani Apalara and Salim Messaoudi Decay of Solution of a Viscoelastic Problem

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Tijani Apalara and Salim Messaoudi Decay of Solution of a Viscoelastic Problem

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The decay results are established in the absence, as well as in the presence of a source term. In this regard, we establish a decay result which depends on the behavior of the external force. This thesis contains five chapters. In Chapter 2, we present some principal concepts, some theorems on Sobolev embeddings and some lemmas which are of essential use in the proofs of our results. The case when the relaxation... The aim of this thesis is to investigate the asymptotic behavior of solutions of some viscoelastic problems in bounded domains. In this regard, we study several problems and establish exponential, polynomial and general decay rate results. In Chapter 1, we discuss the properties and significance of viscoelastic materials and we end the chapter by reviewing some literatures related to our problems. In Chapter 3, we study the asymptotic behaviors of solution of a viscoelastic problem when the relaxation function is decaying exponentially in the presence of a source term.

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