"Internal null controllability of a linear Schrödinger–KdV system on a bounded interval"

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Research areas:
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Year:
2016
Type of Publication:
Article
Keywords:
Dispersive system, Schrödinger equation, Korteweg de Vries equation, Null controllability, Carleman estimates
Authors:
Journal:
Journal of Differential Equations
Volume:
260
Number:
1
Pages:
653-687
Month:
January
ISSN:
0022-0396
Abstract:
The control of a linear dispersive system coupling a Schrödinger and a linear Korteweg–de Vries equation is studied in this paper. The system can be viewed as three coupled real-valued equations by taking real and imaginary parts in the Schrödinger equation. The internal null controllability is proven by using either one complex-valued control on the Schrödinger equation or two real-valued controls, one on each equation. Notice that the single Schrödinger equation is not known to be controllable with a real-valued control. The standard duality method is used to reduce the controllability property to an observability inequality, which is obtained by means of a Carleman estimates approach