Well-posedness and energy decay of a transmission problem of Kirchhoff type wave equations with damping and delay terms

Abstract

We consider a transmission problem of Kirchhoff type wave equations with delay and damping terms, subject to a memory condition on one part of the boundary. Under appropriate hypotheses on the relaxation function and the relationship between weights of damping and delay terms, we establish well-posedness of the problem. Using the Faedo-Galerkin approximation technique, and introducing suitable energyand Lyapunov functionals, we obtain estimates for exponential, polynomial, and logarithmic decay. For more information see https://ejde.math.txstate.edu/Volumes/2021/95/abstr.html