scholarly journals A null controllability problem with a finite number of constraints on the normal derivative for the semilinear heat equation

2012 ◽  
pp. 1-34 ◽  
Author(s):  
Carole Louis-Rose
Keyword(s):  
Heat Equation ◽  
Finite Number ◽  
Normal Derivative ◽  
Null Controllability ◽  
Controllability Problem ◽  
Semilinear Heat Equation

scholarly journals Null controllability for the semilinear heat equation in a non-smooth domain

2015 ◽  
Vol 353 (3) ◽  
pp. 229-234
Author(s):  
Tarik Ali-Ziane ◽  
Zahia Ferhoune ◽  
Ouahiba Zair
Keyword(s):  
Heat Equation ◽  
Null Controllability ◽  
Smooth Domain ◽  
Semilinear Heat Equation

scholarly journals NULL CONTROLLABILITY FOR THE SEMILINEAR HEAT EQUATION IN UNBOUNDED DOMAINS

Pesquimat ◽  
2014 ◽  
Vol 4 (2) ◽  
Author(s):  
Silvano Dias Bezerra de Menezes ◽  
Eugenio Cabanillas Lapa
Keyword(s):  
Heat Equation ◽  
Unbounded Domains ◽  
Null Controllability ◽  
Semilinear Heat Equation

scholarly journals Approximate controllability of the semilinear heat equation

1995 ◽  
Vol 125 (1) ◽  
pp. 31-61 ◽  
Author(s):  
Caroline Fabre ◽  
Jean-Pierre Puel ◽  
Enrike Zuazua
Keyword(s):  
Fixed Point ◽  
Heat Equation ◽  
Bounded Domain ◽  
Variational Approach ◽  
Approximate Controllability ◽  
Nonempty Subset ◽  
Linear Equations ◽  
Fixed Point Method ◽  
Controllability Problem ◽  
Semilinear Heat Equation

This article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain Ω when the control acts on any open and nonempty subset of Ω or on a part of the boundary. In the case of both an internal and a boundary control, the approximate controllability in LP(Ω) for 1 ≦ p < + ∞ is proved when the nonlinearity is globally Lipschitz with a control in L∞. In the case of the interior control, we also prove approximate controllability in C0(Ω). The proof combines a variational approach to the controllability problem for linear equations and a fixed point method. We also prove that the control can be taken to be of “quasi bang-bang” form.

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