Long-time behaviors of wave equations stabilized by boundary memory damping and friction damping

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-10-01 DOI:10.1016/j.cnsns.2024.108377

Chan Li , Li-Jun Wu , Yunchuan Chen , Jia-Yi Li

引用次数: 0

Abstract

In this paper, we study the long-time behaviors of wave equations subject to boundary memory damping and friction damping. Different from assumptions that memory kernel is a nonnegative, monotone function in the previous literatures, we assume that the primitive of the memory kernel is a generalized positive definite kernel (abbreviated to GPDK), which may vary sign or oscillate. The key to the problem lies in establishing the connection between memory damping and energy terms. By combining the properties of the positive definite kernel with classical multiplier methods, and constructing auxiliary systems, we ultimately establish the asymptotic stability, exponential stability and polynomial stability of systems featuring boundary memory damping and friction damping. To illustrate our theoretical results, we provide some numerical simulations.

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利用边界记忆阻尼和摩擦阻尼稳定波方程的长期行为

本文研究了受边界记忆阻尼和摩擦阻尼影响的波方程的长期行为。与以往文献中关于记忆核是一个非负单调函数的假设不同，我们假设记忆核的基元是一个广义正定核（简称 GPDK），它可以改变符号或振荡。问题的关键在于建立记忆阻尼和能量项之间的联系。通过将正定核的特性与经典乘法器方法相结合，并构建辅助系统，我们最终建立了以边界记忆阻尼和摩擦阻尼为特征的系统的渐近稳定性、指数稳定性和多项式稳定性。为了说明我们的理论结果，我们提供了一些数值模拟。

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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.