Year: 2023
Author: Xiaoming Peng, Yadong Shang
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 4 : pp. 349–364
Abstract
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 $$\mu'(s)\le -k_1\mu^m(s), \ 1\le m<\frac{3}{2}$$ we establish the exponential stability result for $m=1$ and the polynomial stability result for $1<m<\frac{3}{2}$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v36.n4.2
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 4 : pp. 349–364
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Exponential stability polynomial stability quasilinear nonlinear damping memory.