Decay rate for systems of $ m $-nonlinear wave equations with new viscoelastic structures

Abstract

<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 ^{[<xref ref-type="bibr" rid="b18">18</xref>,<xref ref-type="bibr" rid="b27">27</xref>]} for system of $ m $-equations inspired from the paper ^{[<xref ref-type="bibr" rid="b1">1</xref>]}. </abstract>