Well-Posedness and Asymptotic Analysis of Wave Equation with Nonlocal Boundary Damping

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-09-30 DOI:10.1007/s00245-025-10327-6

Marcelo M. Cavalcanti, Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Cintya A. Okawa

引用次数: 0

Abstract

In this work, we study a wave equation with nonlocal boundary damping of energy type. We begin by establishing the well-posedness of the problem using the Galerkin method. Next, we investigate the asymptotic behavior of the solution by applying the multiplier method, and we enhance the decay rate through the use of Nakao’s Lemma. Finally, we employ the radial multiplier technique to obtain an optimal polynomial decay rate under this type of damping.

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非局部边界阻尼波动方程的适定性及渐近分析

本文研究了具有能量型非局部边界阻尼的波动方程。我们首先用伽辽金方法建立了问题的适定性。接下来，我们利用乘数法研究了解的渐近行为，并利用Nakao引理提高了衰减率。最后，我们采用径向乘法器技术来获得这种阻尼下的最优多项式衰减率。

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.