Null controllability for parabolic systems with dynamic boundary conditions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/eect.2023051

Mariem Jakhoukh, Lahcen Maniar

引用次数: 0

Abstract

In this paper, we study the null controllability of systems of $ n $-coupled parabolic equations with dynamic boundary conditions, where the coupling and control matrices $ A $ and $ B $ are constant in time and space. Being different to the case of static boundary conditions, we will show that the Kalman rank condition $ rank[B, AB,\dots, A^{n-1}B ] = n $ is a sufficient condition, we also show that it is necessary for the null controlability under an extra assumption on the boundary coupling. The null controlability result will be proved by proving Carleman and observability inequalities for the corresponding adjoint problem.

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具有动态边界条件的抛物型系统的零可控性

本文研究了具有动态边界条件的n -耦合抛物方程系统的零可控性，其中耦合和控制矩阵A和B在时间和空间上都是恒定的。与静态边界条件的情况不同，我们将证明卡尔曼秩条件$ rank[B, AB，\dots, A^{n-1}B] = n $是一个充分条件，并且在边界耦合的额外假设下证明零可控性是必要的。通过对相应伴随问题的Carleman不等式和可观测不等式的证明，证明了零可控性结果。

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

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

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