On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2021-02-09 DOI:10.3934/mcrf.2021039

J. Valein

引用次数: 10

Abstract

The aim of this work is to study the asymptotic stability of the nonlinear Korteweg-de Vries equation in the presence of a delayed term in the internal feedback. We first consider the case where the weight of the term with delay is smaller than the weight of the term without delay and we prove a semiglobal stability result for any lengths. Secondly we study the case where the support of the term without delay is not included in the support of the term with delay. In that case, we give a local exponential stability result if the weight of the delayed term is small enough. We illustrate these results by some numerical simulations.

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具有时滞内反馈的Korteweg-de Vries方程的渐近稳定性

本文的目的是研究非线性Korteweg-de Vries方程在内部反馈中存在时滞项时的渐近稳定性。我们首先考虑有延迟项的权值小于无延迟项的权值的情况，并证明了任意长度的半全局稳定性结果。其次，我们研究了无迟延条款的支持不包括在有迟延条款的支持中的情况。在这种情况下，如果延迟项的权重足够小，我们给出了一个局部指数稳定性的结果。我们通过一些数值模拟来说明这些结果。

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

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.