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Volume 36, Issue 4
Asymptotic Stability for a Quasilinear Viscoelastic Equation with Nonlinear Damping and Memory

Xiaoming Peng & Yadong Shang

DOI: 10.4208/jpde.v36.n4.2

J. Part. Diff. Eq., 36 (2023), pp. 349-364.

Published online: 2023-11

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  • 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 $1<m<\frac{3}{2}$.

  • Keywords

Exponential stability, polynomial stability, quasilinear, nonlinear damping, memory.

  • AMS Subject Headings

35B40, 35L70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-36-349, author = {Peng , Xiaoming and Shang , Yadong}, title = {Asymptotic Stability for a Quasilinear Viscoelastic Equation with Nonlinear Damping and Memory}, journal = {Journal of Partial Differential Equations}, year = {2023}, volume = {36}, number = {4}, pages = {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 $1<m<\frac{3}{2}$.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n4.2}, url = {http://global-sci.org/intro/article_detail/jpde/22133.html} }
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 -

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 $1<m<\frac{3}{2}$.

Xiaoming Peng & Yadong Shang. (2023). Asymptotic Stability for a Quasilinear Viscoelastic Equation with Nonlinear Damping and Memory. Journal of Partial Differential Equations. 36 (4). 349-364. doi:10.4208/jpde.v36.n4.2
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