Boundary null controllability for the heat equation with dynamic boundary conditions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-06-21 DOI:10.3934/eect.2022041

Salah-Eddine Chorfi, G. E. Guermai, A. Khoutaibi, L. Maniar

引用次数: 2

Abstract

In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control supported on an arbitrary subboundary. The proof of the main result combines a new boundary Carleman estimate and some regularity estimates for the adjoint system, with an explicit dependence with respect to the final time. This technique allows us to overcome a new difficulty that arises when absorbing a normal derivative term.

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具有动态边界条件的热方程的边界零可控性

本文研究了具有动态边界条件的热方程的边界可控性问题。更准确地说，我们利用支持在任意子边界上的边界控制，证明了方程在任意正时刻是零可控的。主要结果的证明结合了一个新的边界Carleman估计和一些伴随系统的正则性估计，与最终时间有显式的依赖关系。这种技术使我们能够克服吸收正规导数项时出现的新困难。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.