Exponential stability for a nonlinear porous-elastic system with delay

TL;DR

This paper investigates the existence, uniqueness, and exponential decay of solutions in a nonlinear porous-elastic system with delay, using semigroup theory and Lyapunov functionals.

Contribution

It introduces a novel analysis of a nonlinear porous-elastic system with delay, establishing conditions for global solutions and exponential stability.

Findings

Existence and uniqueness of global solutions are proven.

Exponential decay of the system's energy is established.

Conditions relating system coefficients are identified for stability.

Abstract

In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to obtain the existence and uniqueness of a global solution, we will use the semigroup theory of linear operators and under a certain relation involving the coefficients of the system together with a Lyapunov functional, we will establish the exponential decay of the energy associated to the system.