Asymptotic stability for a viscoelastic equation with nonlinear damping and very general type of relaxation functions (Q2294610)

The authors consider a viscoelastic equation with a nonlinear frictional damping, containing a so-called relaxation term in integral form. Such time integral involves the Laplacian with coefficient given by a function satisfying some growth conditions. The existence of a unique weak solution is proved by means of the Galerkin method. The main results of the paper are some decay results on the energy, depending on the relaxation function.