General decay of solutions for a weak viscoelastic equation with acoustic boundary conditions

In this paper, we consider the weak viscoelastic equation with a homogeneous Dirichlet condition on a portion of the boundary and acoustic boundary conditions on the rest of the boundary. We establish a general decay result, which depends on the behavior of both alpha and g, by using the perturbed energy functional technique. This is an extension and improvement of the previous result from Park and Park (Nonlinear Anal 74(3):993-998, 2011) (i.e., the similar problem with ) to the time-dependent viscoelastic case.