A nonautonomous delayed viscoelastic wave equation with a linear damping: well-posedness and exponential stability

Djemoui, Marwa; Chellaoua, Houria; Boukhatem, Yamna

doi:10.22124/jmm.2024.26420.2331

A nonautonomous delayed viscoelastic wave equation with a linear damping: well-posedness and exponential stability

Document Type : Research Article

Authors

¹ Laboratory of Pure and Applied Mathematics, University of Laghouat, Laghouat, Algeria

² Department of Mathematics and Computer Science. Faculty of Science and Technology, University of Ghardaia, Ghardaia, Algeria. Laboratory of Pure and Applied Mathematics, University of Laghouat, Laghouat, Algeria

³ National Higher School of Mathematics, Mahelma, Sidi Abdellah, Algeria. Laboratory of Pure and Applied Mathematics, University of Laghouat, Laghouat, Algeria

10.22124/jmm.2024.26420.2331

Abstract

In this paper, we consider a nonautonomous viscoelastic wave equation with linear damping and delayed terms. Under some appropriate assumptions, we prove the global existence using the semi-group theory. Furthermore, for a small enough coefficient of delay, we obtained a stability result via a suitable Lyapunov function where the kernel function decays exponentially.

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