Global Conference on Mathematics and Applications (GCMA)

We consider a nonlinear viscoelastic equation involving both a memory term and an internal time-delay effect. The interaction between memory and delay introduces additional difficulties in the analysis of the long-time behavior of solutions. Under suitable assumptions on the relaxation kernel and the delay parameters, the existence of a global solution is established by means of the Faedo–Galerkin approximation method. To investigate the asymptotic behavior, an appropriate Lyapunov functional is constructed by incorporating the contributions of both the memory and delayed terms. Through suitable differential inequalities, generalized decay estimates for the energy are derived. The obtained results provide a unified description of the stabilization of nonlinear viscoelastic systems under memory-delay coupling and allow for a broad class of energy decay rates.