Uniform stabilization of semilinear wave equations with localized internal damping and dynamic Wentzell boundary conditions with a memory term

Abstract

In this paper, we deal with the semilinear wave equations with a local internal damping and dynamic Wentzell boundary conditions with a memory term. The stabilization estimate is more difficult to obtain since the physical energy of the system not only contains the $$H^1$$ Sobolev norm of the solution but also depends on the memory term on the boundary. The exponential stabilization is attained by constructing new Lyapunov functionals and using multiplier methods. To illustrate the results, numerical simulations are given in the last part.