On the Exact Boundary Controllability of Semilinear Wave Equations

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-07-03 DOI:10.1137/23m1586598

Sue Claret, Jérôme Lemoine, Arnaud Münch

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 1953-1976, August 2024.
Abstract. We address the exact boundary controllability of the semilinear wave equation [math] posed over a bounded domain [math] of [math]. Assuming that [math] is continuous and satisfies the condition [math] for some [math] small enough and some [math] in [math], we apply the Schauder fixed point theorem to prove the uniform controllability for initial data in [math]. Then, assuming that [math] is in [math] and satisfies the condition [math], we apply the Banach fixed point theorem and exhibit a strongly convergent sequence to a state-control pair for the semilinear equation.

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论半线性波方程的精确边界可控性

SIAM 控制与优化期刊》，第 62 卷第 4 期，第 1953-1976 页，2024 年 8 月。摘要。我们讨论在[math]的有界域[math]上提出的半线性波方程[math]的精确边界可控性。假设[math]是连续的，并且满足[math]中一些足够小的[math]和[math]中一些[math]的条件[math]，我们应用 Schauder 定点定理证明[math]中初始数据的均匀可控性。然后，假设[math]在[math]中并满足[math]条件，我们应用巴拿赫定点定理，展示了半线性方程状态-控制对的强收敛序列。

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

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.