Exponential stabilization of the transmission wave equation with dynamical boundary conditions and a delay term

Abstract

In this paper, we consider stabilization of transmission of the wave equation with dynamical boundary conditions that include a delay term acts on the boundary. By introducing suitable energy function, we prove under some assumptions that the closed‐loop system is exponentially stable. In addition, we also consider the situation where the above system is controlled by distributed feedback near the transmission boundary and can also obtain exponential stability estimates with fewer assumptions.