Abstract
The article discusses the effect of weak and strong damping terms on decay rate for systems of nonlinear m- wave equations with new viscoelastic structures. The factors that allowed system (1.1) to coexist for a long time are the strong nonlinearities in the sources. We showed, under a novel condition on the kernel function in (2.4), a new scenario for energy decay in (3.7) by using an appropriate energy estimates. This result extend the results in [18, 27] for system of m-equations inspired from the paper [1].