BOUNDARY NULL CONTROLLABILITY OF THE HEAT EQUATION WITH WENTZELL BOUNDARY CONDITION AND DIRICHLET CONTROL

被引：0

作者：

Chorfi, Salah-eddine ^{[1
]}

Ismailov, Mansur i. ^{[3
,4
]}

Maniar, Lahcen ^{[1
,2
]}

Oner, Isil ^{[3
]}

机构：

[1] Cadi Ayyad Univ, Fac Sci Semlalia, Lab Math Modeling & Automat Syst, Dept Math,UCA, BP 2390, Marrakech, Morocco

[2] Univ Mohammed VI Polytech, Vanguard Ctr, Benguerir, Morocco

[3] Gebze Tech Univ, Dept Math, TR-41400 Gebze, Kocaeli, Turkiye

[4] Khazar Univ, Ctr Math & Its Applicat, Baku, Azerbaijan

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2025年

关键词：

Heat equation; Wentzell condition; null controllability; moment method; Hilbert uniqueness method; PARABOLIC EQUATIONS; OPERATORS;

D O I：

10.3934/eect.2025058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. We consider the linear heat equation with a Wentzell-type boundary condition and a Dirichlet control. Such a boundary condition can be reformulated as one of dynamic type. First, we formulate the boundary controllability problem of the system within the framework of boundary control systems, proving its well-posedness. Then, we reduce the question to a moment problem. Using the spectral analysis of the associated Sturm-Liouville problem and the moment method, we establish the null controllability of the system at any positive time T. Finally, we approximate minimum energy controls by a penalized HUM approach. This allows us to validate the theoretical controllability results obtained by the moment method.

引用

页数：20

共 43 条

[1]

Ammar-Khodja F., 2018, Evolution Equations, V439, P1

[2]

Arendt W., 2012, Oper. Theory Adv. App., V221, P47

[3] NULL CONTROLLABILITY FOR BACKWARD STOCHASTIC PARABOLIC CONVECTION-DIFFUSION EQUATIONS WITH DYNAMIC BOUNDARY CONDITIONS [J].