Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Well-posedness, regularity and exact controllability for the problem of transmission of the Schrödinger equation


Authors: I. Allag and S. E. Rebiai
Journal: Quart. Appl. Math. 72 (2014), 93-108
MSC (2000): Primary 35J10, 93C20, 93C25, 93D15, 93B05, 93B07
DOI: https://doi.org/10.1090/S0033-569X-2013-01351-0
Published electronically: November 13, 2013
MathSciNet review: 3185134
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Abstract: In this paper, we shall study the system of transmission of the Schrödinger equation with Dirichlet control and colocated observation. Using the multiplier method, we show that the system is well-posed with input and ouput space $ U=L^{2}(\Gamma )$ and state space $ X=H^{-1}(\Omega ).$ The regularity of the system is also established, and the feedthrough operator is found to be zero. Finally, the exact controllability of the open-loop system is obtained by proving the observability inequality of the dual system.


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Additional Information

I. Allag
Affiliation: Department of Mathematics, Faculty of Sciences, University of Batna, 05000 Batna, Algeria
Email: allag{\textunderscore}ismahane@hotmail.com

S. E. Rebiai
Affiliation: Department of Mathematics, Faculty of Sciences, University of Batna, 05000 Batna, Algeria
Email: rebiai@hotmail.com

DOI: https://doi.org/10.1090/S0033-569X-2013-01351-0
Received by editor(s): March 14, 2012
Published electronically: November 13, 2013
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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