Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2024-04-22 DOI:10.1007/s10440-024-00650-5

K. Laoubi, D. Seba

引用次数: 0

Abstract

This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the square. After reformulating this problem into an abstract Cauchy problem, we show the existence and uniqueness of the solution. Then, by analyzing a family of eigenvalues of the corresponding operator, we prove that the rate of energy decay decreases in a polynomial way.

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带动力学边界条件的波方程的多项式能量衰减率

本文研究的是耗散波方程的多项式衰减问题，该方程受动力学边界条件和方形非忽略密度的限制。在将这一问题重新表述为一个抽象的 Cauchy 问题后，我们证明了解的存在性和唯一性。然后，通过分析相应算子的特征值族，我们证明了能量衰减率以多项式方式下降。

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

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.