Asymptotic behavior for a weak viscoelastic wave equations with a dynamic boundary and time varying delay term

Abstract

In this paper, we consider the weak viscoelastic wave equations with dynamic boundary conditions related to the Kelvin Voigt damping and delay term acting on the boundary in a bounded domain. Under appropriate conditions on μ 1 and μ 2 , we prove the asymptotic behavior by making use an appropriate Lyapunov functional.

Measure functional differential equations with infinite time‐dependent delay

“…On the other hand, recently many authors have begun to study functional differential equations with time-dependent delay (see [5,11,13,15,22]). These equations have shown to be useful tools for applications, since they can describe more precisely certain environment phenomena.…”

Existence and decay rates for a coupled Balakrishnan‐Taylor viscoelastic system with dynamic boundary conditions

“…For results on single wave equation with Balakrishnan‐Taylor damping , the existence of solutions and energy decay were well established; see, for instance, Clark, Feng and Kang, Ha, Kang, Park, Tatar and Zaraï, Wu, You, Zaraï and Tatar, and so on. With respect to wave equation with dynamic boundary conditions, the energy decay of solutions to wave equation with finite and infinite memories were considered by Cavalcanti et al, Feng, Ferhat and Hakem, Gerbi and Said‐Houari, Li et al, Messaoudi and Mustafa, Messaoudi and Al‐Gharabli, Wu, Zaraï et al, and so on.…”