Exponential Stability of Transmission Problem With Distributed Delay and Memory Terms

In this paper, under appropriate assumptions on the nonlinear weights and , the balance relationship between damping and distributed delay as well as that between damping and memory terms is investigated. Under such balance conditions, the well‐posedness is proved by combining the semigroup approach and the Kato operator perturbation technique. Then, in line with the multiplier method, the exponential stability of the problem is obtained through the construction of an appropriate Lyapunov functional.