Electron. J. Diff. Equ., Vol. 2016 (2016), No. 74, pp. 1-12.

Null controllability of a cascade system of Schrodinger equations

Marcos Lopez-Garcia, Alberto Mercado, Luz de Teresa

This article presents a control problem for a cascade system of two linear N-dimensional Schrodinger equations. We address the problem of null controllability by means of a control supported in a region not satisfying the classical geometrical control condition. The proof is based on the application of a Carleman estimate with degenerate weights to each one of the equations and a careful analysis of the system in order to prove null controllability with only one control force.

Submitted August 7, 2015. Published March 17, 2016.
Math Subject Classifications: 93B05, 93C20.
Key Words: Null controllability; coupled equations; Schrodinger equation; non geometrical condition; Carleman inequality.

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  Marcos López-García
Instituto de Matemáticas-Unidad Cuernavaca
Universidad Nacional Autónoma de México
Apdo. Postal 273-3, Cuernavaca Mor. CP 62251, México
email: flopez@matem.unam.mx
  Alberto Mercado
Departamento de Matemática
Universidad Técnica Federico Santa María
Casilla 110-V, Valparaíso, Chile
email: alberto.mercado@usm.cl
Luz de Teresa
Instituto de Matemáticas
Universidad Nacional Autónoma de México
Circuito Exterior, CU, 04510 México
email: ldeteresa@im.unam.mx

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