The cost of approximate controllability of heat equation with general dynamical boundary conditions

被引：12

作者：

Boutaayamou, Idriss ^{[1
]}

Chorfi, Salah-Eddine ^{[2
]}

Maniar, Lahcen ^{[2
]}

Oukdach, Omar ^{[2
]}

机构：

[1] Univ Ibn Zohr, Fac Polydisciplinaires Ouarzazate, Dept Math Informat & Gest, BP 638, Ouarzazate 45000, Morocco

[2] Cadi Ayyad Univ, Fac Sci Semlalia, UMMISCO IRD UPMC, LMDP, BP 2390, Marrakech, Morocco

来源：

PORTUGALIAE MATHEMATICA | 2021年 / 78卷 / 01期

关键词：

Cost of approximate controllability; Carleman estimates; observability inequality; dynamic boundary conditions; SYSTEMS;

D O I：

10.4171/PM/2061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the heat equation with dynamic boundary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and some optimization techniques, we obtain explicit bounds of the minimal norm control. We consider the linear and the semilinear cases.

引用

页码：65 / 99

页数：35

共 50 条

[1] APPROXIMATE BOUNDARY CONTROLLABILITY FOR HEAT EQUATION
MACCAMY, RC
MIZEL, VJ
SEIDMAN, TI
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1968, 23 (03) : 699 - &
[2] IMPULSE NULL APPROXIMATE CONTROLLABILITY FOR HEAT EQUATION WITH DYNAMIC BOUNDARY CONDITIONS
Chorfi, Salah-Eddine
El Guermai, Ghita
Maniar, Lahcen
Zouhair, Walid
[J]. MATHEMATICAL CONTROL AND RELATED FIELDS, 2023, 13 (03) : 1023 - 1046
[3] Approximate controllability of the semilinear heat equation: boundary control
Zuazua, E
[J]. COMPUTATIONAL SCIENCE FOR THE 21ST CENTURY, 1997, : 738 - 747
[4] APPROXIMATE BOUNDARY CONTROLLABILITY OF HEAT EQUATION, .2.
MACCAMY, RC
MIZEL, VJ
SEIDMAN, TI
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1969, 28 (03) : 482 - &
[5] Approximate controllability of the wave equation with mixed boundary conditions
Pestov L.
Strelnikov D.
[J]. Journal of Mathematical Sciences, 2019, 239 (1) : 75 - 85
[6] Note on the cost of the approximate controllability for the heat equation with potential
Phung, KD
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 295 (02) : 527 - 538
[7] BOUNDARY NULL CONTROLLABILITY FOR THE HEAT EQUATION WITH DYNAMIC BOUNDARY CONDITIONS
Chorfi, Salah-Eddine
EL Guermai, Ghita
Khoutaibi, Abdelaziz
Maniar, Lahcen
[J]. EVOLUTION EQUATIONS AND CONTROL THEORY, 2023, 12 (02): : 542 - 566
[8] STACKELBERG-NASH NULL CONTROLLABILITY OF HEAT EQUATION WITH GENERAL DYNAMIC BOUNDARY CONDITIONS
Boutaayamou, Idriss
Maniar, Lahcen
Oukdach, Omar
[J]. EVOLUTION EQUATIONS AND CONTROL THEORY, 2021, : 1285 - 1307
[9] Null controllability for a heat equation with periodic boundary conditions
Oner, Isil
[J]. UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 2021, 83 (04): : 13 - 22
[10] NULL CONTROLLABILITY FOR A HEAT EQUATION WITH PERIODIC BOUNDARY CONDITIONS
Oner, Isil
[J]. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2021, 83 (04): : 13 - 22

← 1 2 3 4 5 →