Arbitrary rate of decay for a viscoelastic equation with acoustic boundary conditions

In this paper we consider the viscoelastic equation with a homogeneous Dirichlet condition on a portion of the boundary and acoustic boundary conditions on the rest of the boundary. By using the assumptions on the relaxation function due to Tatar (2011), we generalize the work of Park and Park (2011) to an arbitrary rate of decay with not necessarily of an exponential or polynomial one and without the assumption condition ∫0∞g(s)ds<12.