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A system of viscoelastic wave equations of Kirchhoff type is considered. For a wider class of relaxation functions, we use spaces weighted by the density function to establish a very general decay rate of the solution.

In this paper, we consider a transmission problem in the presence of history and delay terms.Under appropriate assumptions, we prove well-posedness by using the semigroup theory. Our stability estimate proves that the unique dissipation given by the history term is strong enough to stabilize exponentially the system in presence of delay by introducing a suitable Lyaponov functional.

Here, a system of 3 wave equations in Rn with infinite memories acting in the first 2 equations is considered. Using weighted spaces, we prove the polynomial stability of the system under some conditions on μ1,μ2, and ϕ as t→∞.