Boundary null controllability for the heat equation with dynamic boundary conditions

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory 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

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology