In this work we investigate a viscoelastic wave equation involving a logarithmic nonlinearity and acoustic boundary conditions. Making some assumptions on the memory kernel function g, which is not necessarily decreasing and using Lyapunov method, we establish a general decay estimate of the solution.

In this paper, we deal with the wave equation with acoustic boundary conditions. The exponential stabilization is obtained by Lyapunov approach and Riemannian geometry method. We then apply our main theorem to the wave equations with memory type acoustic boundary conditions, which is not available in the literature and give an example in the end.