Long-Time Stabilization of Solutions to the Semilinear Viscoelastic Wave Equation with Analytic Nonlinearity and Time Varying Delay

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-06-09 DOI:10.1007/s00245-025-10274-2

Hassan Yassine

引用次数: 0

Abstract

We consider the nonautonomous viscoelastic wave equation with analytic nonlinearity and time varying delay. By construction of a suitable Lyapunov energy and by using the Łojasiewicz-Simon inequality we show that, when the amplitude of the time delay is small enough, the dissipation given by the viscoelastic term is strong enough to prove the convergence to equilibrium as well as estimates for the rate of convergence for any global bounded solution.

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具有解析非线性和时变时滞的半线性粘弹性波动方程解的长时间镇定性

考虑具有解析非线性和时变时滞的非自治粘弹性波动方程。通过构造合适的Lyapunov能量并利用Łojasiewicz-Simon不等式证明，当时滞幅值足够小时，粘弹性项给出的耗散足够强，足以证明对任何全局有界解的收敛性以及收敛速度的估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.