Logarithmic convexity and impulsive controllability for the one-dimensional heat equation with dynamic boundary conditions

被引：8
作者：
Chorfi, Salah-Eddine [1 ]
El Guermai, Ghita [1 ]
Maniar, Lahcen [1 ]
Zouhair, Walid [1 ]
机构：
[1] Cadi Ayyad Univ, LMDP UMMISCO IRD UPMC, Fac Sci Semlalia, BP 2390, Marrakech, Morocco
来源：
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION | 2022年 / 39卷 / 03期
关键词：
Impulsive approximate controllability; impulsive control problems; Carleman commutator; logarithmic convexity; dynamic boundary conditions; Hilbert Uniqueness Method; APPROXIMATE CONTROLLABILITY; NULL CONTROLLABILITY; PARABOLIC EQUATIONS;
D O I：
10.1093/imamci/dnac013
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for the one-dimensional heat equation with dynamic boundary conditions. Consequently, we establish the impulse approximate controllability for the impulsive heat equation with dynamic boundary conditions. Moreover, we obtain an explicit upper bound of the cost of impulse control. At the end, we give a constructive algorithm for computing the impulsive control of minimal L-2-norm. We also present some numerical tests to validate the theoretical results and show the efficiency of the designed algorithm.
引用
收藏
页码：861 / 891
页数：31
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