On the existence and decay of a viscoelastic system with variable-exponent nonlinearity

In the present paper, we discuss the existence and the long-time behavior of a system of two viscoelastic equations with variable-exponent nonlinearities acting in both equations. First, we establish in details the existence of solutions, then prove explicit and general decay results, under a very general assumption on the relaxation function and for suitable given data, to solutions with enough regularities. Our results extend and generalize many earlier results in the literature.