Exact Controllability For Korteweg-De Vries Equation and its Cost in the Zero-Dispersion Limit

2015 ◽  
pp. 293-306
Author(s):  
Hajer Dbebria ◽  
Ali Salem
Keyword(s):  
Vries Equation ◽  
Exact Controllability ◽  
De Vries ◽  
Dispersion Limit

scholarly journals Exact Controllability of a Linear Korteweg--de Vries Equation by the Flatness Approach

2019 ◽  
Vol 57 (4) ◽  
pp. 2467-2486 ◽  
Author(s):  
Philippe Martin ◽  
Ivonne Rivas ◽  
Lionel Rosier ◽  
Pierre Rouchon
Keyword(s):  
Vries Equation ◽  
Exact Controllability ◽  
De Vries

GLOBAL CONTROLLABILITY OF A NONLINEAR KORTEWEG–DE VRIES EQUATION

2009 ◽  
Vol 11 (03) ◽  
pp. 495-521 ◽  
Author(s):  
MARIANNE CHAPOULY
Keyword(s):  
Boundary Control ◽  
Vries Equation ◽  
Boundary Value ◽  
Exact Controllability ◽  
Left Endpoint ◽  
Bounded Interval ◽  
First Derivative ◽  
De Vries ◽  
Positive Time ◽  
The Right

We are interested in both the global exact controllability to the trajectories and in the global exact controllability of a nonlinear Korteweg–de Vries equation in a bounded interval. The local exact controllability to the trajectories by means of one boundary control, namely the boundary value at the left endpoint, has already been proved independently by Rosier, and Glass and Guerrero. We first introduce here two more controls: the boundary value at the right endpoint and the right member of the equation, assumed to be x-independent. Then, we prove that, thanks to these three controls, one has the global exact controllability to the trajectories, for any positive time T. Finally, we introduce a fourth control on the first derivative at the right endpoint, and we get the global exact controllability, for any positive time T.

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