scholarly journals Internal null-controllability of the N -dimensional heat equation in cylindrical domains

2015 ◽  
Vol 353 (10) ◽  
pp. 925-930
Author(s):  
El Hadji Samb
Keyword(s):  
Heat Equation ◽  
Null Controllability ◽  
Cylindrical Domains

scholarly journals Null controllability of a nonlinear heat equation

2002 ◽  
Vol 7 (7) ◽  
pp. 375-383 ◽  
Author(s):  
G. Aniculăesei ◽  
S. Aniţa
Keyword(s):  
Heat Equation ◽  
Dirichlet Boundary ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Nonlinear Heat Equation ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Linearized System ◽  
Kakutani Fixed Point ◽  
Exact Null Controllability ◽  
Kakutani Fixed Point Theorem

We study the internal exact null controllability of a nonlinear heat equation with homogeneous Dirichlet boundary condition. The method used combines the Kakutani fixed-point theorem and the Carleman estimates for the backward adjoint linearized system. The result extends to the case of boundary control.

scholarly journals Null controllability of the heat equation in pseudo-cylinders by an internal control

2020 ◽  
Vol 26 ◽  
pp. 122
Author(s):  
Jon Asier Bárcena-Petisco
Keyword(s):  
Heat Equation ◽  
Internal Control ◽  
Cylindrical Part ◽  
Null Controllability ◽  
Carleman Estimate ◽  
Main Difficulty ◽  
Absorption Properties ◽  
Weighted Function ◽  
Cylindrical Structure ◽  
Linear Heat

In this paper we prove the null controllability of the heat equation in domains with a cylindrical part and limited by a Lipschitz graph. The proof consists mainly on getting a Carleman estimate which presents the usual absorption properties. The main difficulty we face is the loss of existence of the usual weighted function in C2 smooth domains. In order to deal with this, we use its cylindrical structure and approximate the system by the same system stated in regular domains. Finally, we show some applications like the controllability of the semi-linear heat equation in those domains.

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