Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 95, pp. 1-23.

Title: Well-posedness and  energy decay of a transmission problem of Kirchhoff type
wave equations with damping and delay terms
       
Authors: Zhiqing Liu (Qingdao Univ.y of Science and Tech., Qingdao, China)
         Cunchen Gao (Ocean Univ. of China, Qingdao, China)
         Zhong Bo Fang (Ocean Univ. of China, Qingdao, China)

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 energy
and Lyapunov functionals, we obtain estimates for  exponential,
polynomial, and logarithmic decay.

Submitted April 5, 2021. Published December 02, 2021.
Math Subject Classifications: 35B40, 35L51.
Key Words: Transmission problem; Kirchhoff type wave equations; damping;
           delay term;  well-posed;  decay estimate.