Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity

Fuente: arXiv
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Main Authors: Peng, Qingqing, Liu, Yikan
Format: Preprint
Published: 2025
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author Peng, Qingqing
Liu, Yikan
author_facet Peng, Qingqing
Liu, Yikan
contents This paper is concerned with the energy decay of a viscoelastic variable coefficient wave equation with nonlocality in time as well as nonlinear damping and polynomial nonlinear terms. Using the Lyapunov method, we establish a polynomial energy decay for the solution under relatively weak assumptions regarding the kernel of the nonlocal term. More specifically, we improve the decay rate of the energy by additionally imposing a certain convexity assumption on the kernel. Several examples are provided to confirm such improvements to faster polynomial or even exponential decays.
format Preprint
id arxiv_https___arxiv_org_abs_2503_07350
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity
Peng, Qingqing
Liu, Yikan
Analysis of PDEs
35L20, 35L70, 35B40
This paper is concerned with the energy decay of a viscoelastic variable coefficient wave equation with nonlocality in time as well as nonlinear damping and polynomial nonlinear terms. Using the Lyapunov method, we establish a polynomial energy decay for the solution under relatively weak assumptions regarding the kernel of the nonlocal term. More specifically, we improve the decay rate of the energy by additionally imposing a certain convexity assumption on the kernel. Several examples are provided to confirm such improvements to faster polynomial or even exponential decays.
title Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity
topic Analysis of PDEs
35L20, 35L70, 35B40
url https://arxiv.org/abs/2503.07350