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arXiv · 2503.07350

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

Qingqing Peng·Yikan Liu
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Abstract

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.

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Qingqing Peng, Yikan Liu. 2025-03-10. Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity. https://doi.org/10.1080/00036811.2025.2500622

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