Exact boundary controllability of the Korteweg–de Vries equation with a piecewise constant main coefficient

2016 ◽  
Vol 97 ◽  
pp. 157-162 ◽  
Author(s):  
Emmanuelle Crépeau
Keyword(s):  
Vries Equation ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Piecewise Constant ◽  
Exact Boundary ◽  
De Vries

Exact boundary controllability for Korteweg-de Vries equation

2009 ◽  
Author(s):  
Ali Salem ◽  
Lotfi Beji ◽  
Samir Otmane ◽  
Azgal Abichou
Keyword(s):  
Vries Equation ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Exact Boundary ◽  
De Vries

ON THE CONTROLLABILITY OF A COUPLED SYSTEM OF TWO KORTEWEG–DE VRIES EQUATIONS

2009 ◽  
Vol 11 (05) ◽  
pp. 799-827 ◽  
Author(s):  
SORIN MICU ◽  
JAIME H. ORTEGA ◽  
ADEMIR F. PAZOTO
Keyword(s):  
Unique Continuation ◽  
Coupled System ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Weakly Nonlinear ◽  
Exact Boundary ◽  
Unique Continuation Property ◽  
De Vries ◽  
Linearized System ◽  
Controllability Property

This paper proves the local exact boundary controllability property of a nonlinear system of two coupled Korteweg–de Vries equations which models the interactions of weakly nonlinear gravity waves (see [10]). Following the method in [24], which combines the analysis of the linearized system and the Banach's fixed point theorem, the controllability problem is reduced to prove a nonstandard unique continuation property of the eigenfunctions of the corresponding differential operator.

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