Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay

2015/07/31 by Danhua Wang, Gang Li, Wang, Danhua +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1507.08855

arxiv created 2015/07/31 · arxiv updated 2015/08/03

Abstract

In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and a delay term. Under appropriate hypothesis on the relaxation function and the relationship between the weight of the damping and the weight of the delay, we prove the well-posedness result by using Faedo-Galerkin method. By introducing suitable Lyaponov functionals, we establish a general decay result, from which the exponential and polynomial types of decay are only special cases.

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