TY - JOUR
T1 - Asymptotic Stability for a Quasilinear Viscoelastic Equation with Nonlinear Damping and Memory
AU - Peng , Xiaoming
AU - Shang , Yadong
JO - Journal of Partial Differential Equations
VL - 4
SP - 349
EP - 364
PY - 2023
DA - 2023/11
SN - 36
DO - http://doi.org/10.4208/jpde.v36.n4.2
UR - https://global-sci.org/intro/article_detail/jpde/22133.html
KW - Exponential stability, polynomial stability, quasilinear, nonlinear damping, memory.
AB - <p style="text-align: justify;">This paper is concerned with the asymptotic behavior of a quasilinear viscoelastic equation with nonlinear damping and memory. Assuming that the kernel $\mu (s)$ satisfies $$\mu&#39;(s)\le -k_1\mu^m(s), \ 1\le m&lt;\frac{3}{2}$$<span style="text-align: justify; text-wrap: wrap;">&nbsp;</span>we establish the exponential stability result for $m=1$ and the polynomial stability result for $1&lt;m&lt;\frac{3}{2}$.</p>