Exponential Stability of Swelling Porous Elastic with a Viscoelastic Damping and Distributed Delay Term

Abstract

In this paper, we consider a swelling porous elastic system with a viscoelastic damping and distributed delay terms in the second equation. The coupling gives new contributions to the theory associated with asymptotic behaviors of swelling porous elastic soils. The general decay result is established by the multiplier method.

Stability and asymptotic behavior of the 3D Boussinesq equations with MHD convection

“…As is remarked by Wu and Zhang, 7 the global well-posedness of the system in R 3 is an open problem. During the past 30 years, a large number of mathematicians and physicians have paid considerable attention to the stability and large time behavior problems near some physically steady states because of the significance and applications in physics and mathematics.…”

General energy decay estimate for a viscoelastic damped swelling porous elastic soils with time delay

“…Apalara et al [19] looked at system () with $$$$ {G}_1={\xi}_1{z}_t\left(x,t\right)+{\xi}_2{z}_t\left(x,t-\tau \right),{G}_2=0,\kern.5em {F}_1=-{\int}_0^tg\left(t-s\right){z}_{xx}\left(x,s\right) ds,\kern.5em {F}_2=0 $$$$ and satisfied the general stability result. Some other authors investigated related studies (see earlier works [17,20–26]). In this work , we focus on system () with $$$$ {G}_1=0,\kern.5em {G}_2=-\left({\xi}_1{u}_t\left(x,t\right)+{\xi}_2{u}_t\left(x,t-\tau \right)\right),\kern.5em {F}_1=0,\kern.5em {F}_2=-{\int}_0^tg\left(t-s\right){u}_{xx}\left(x,s\right) ds, $$$$ where $$$ {\xi}_1 $$$ is a positive consta...…”

“…and satisfied the general stability result. Some other authors investigated related studies (see earlier works [17,[20][21][22][23][24][25][26]).…”

Exponential Stabilization of a Swelling Porous-Elastic System with Microtemperature Effect and Distributed Delay

“…Also, there are many works that have studied this type of problems, of which [11,[15][16][17][18][19][20][21][22][23][24].…”