In this paper, we prove a stability result for the wave equation with viscoelastic and frictional boundary damping. Here the domain \(\Omega \subset {\mathbb {R}}^N\) , \(N\ge 2\) , is a bounded open set with boundary \(\Gamma =\Gamma _0\cup \Gamma _1\) , meas \((\Gamma _0)\) and meas \((\Gamma _1)\) are positive and such that \({\overline{\Gamma }}_0\cap {\overline{\Gamma }}_1\ne \emptyset \) . The presence of singularities and a time-dependent boundary memory term bring several technical difficulties, and new calculations are necessary to combine an appropriate method and the techniques of Bey et al. (J Math Pures Appl 78:1043–1067, 1999) and Grisvard (J Math pures et appl 68: 215–259, 1989).
