Well posedness and exponential stability in a wave equation with a strong damping and a strong delay

Abstract

In this paper, we consider a wave equation with a strong damping and a strong constant (respectively, distributed) delay. We prove the well-posedness and establish an exponential decay result under a suitable assumption on the weight of the damping and the weight of the delay.

Exponential Stability of a Transmission Problem with History and Delay

“…On the contrary, if (5) does not hold, they found a sequence of delays for which the corresponding solution of (4) will be unstable. In [11], authors considered the equation…”

A two-phase flow model with delays

“…They appear in applications such as physics, biology, epidemics, fluid control, transport and population models. Because of their importance, differential equations with delays have received considerable attention, [15,3,5,6,7,16,8,17,20,22]. In real world applications, to control a system by applying some type of external forces, it is natural that these forces take into account not only the present state of the system, but also its history, [3].…”

General decay for viscoelastic plate equation with p-Laplacian and time-varying delay

“…With respect to wave equation with strong time delay, there is just little published work. Messaoudi et al [24] considered the following wave equation with strong time delay:…”

“…However, to the best of my knowledge, there is no stability result for the viscoelastic plate equation with strong time-varying delay. Motivated by [24,25], we study a general decay result for viscoelastic plate equation with p-Laplacian and time-varying delay (1.1)-(1.4) for relaxation function g satisfying the condition (1.9). This result improves on earlier ones in the literature because it allows for certain relaxation functions which are not necessarily of exponential or polynomial decay.…”