Global existence and energy decay of solutions to a viscoelastic wave equation with a delay term in the non-linear internal feedback
by Abbes Benaissa; Aissa Benguessoum; Salim A. Messaoudi
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 5, No. 1, 2014

Abstract: We consider the viscoelastic wave equation in a bounded domain with a delay term in the non-linear internal feedback u_tt(x,t)−Δ_xu(x,t)+∫^t₀h(t−s)Δ_xu(x,s)ds+μ₁g₁(u_t(x,t))+μ₂g₂(u_t(x,t−τ))=0 and prove a global existence result using the energy method combined with the Faedo-Galerkin procedure under assumption of a relation between the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study the asymptotic behaviour of solutions using a perturbed energy method.

Online publication date: Wed, 29-Apr-2015

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