Internal null controllability for the one-dimensional heat equation with dynamic boundary conditions

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

IMA Journal of Mathematical Control and Information Pub Date : 2024-04-30 DOI:10.1093/imamci/dnae015

El Mustapha Ait Ben Hassi, Mariem Jakhoukh, Lahcen Maniar, Walid Zouhair

引用次数: 0

Abstract

The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an observability inequality for the corresponding backward system. In conclusion, the paper includes a set of numerical experiments that serve to confirm the validity of the theoretical findings and underscore the effectiveness of the designed control with a minimal $L^{2}$-norm.

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具有动态边界条件的一维热方程的内部无效可控性

本文的主要重点是为具有动态边界条件的一维热方程建立内部空可控性。这一成果是通过引入新的卡勒曼估计和相应后向系统的可观测性不等式实现的。最后，本文通过一组数值实验证实了理论发现的正确性，并强调了所设计的具有最小 $L^{2}$ 准则的控制的有效性。

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

IMA Journal of Mathematical Control and Information 工程技术-应用数学

CiteScore

3.30

自引率

6.70%

发文量

审稿时长

>12 weeks

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