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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 78192, 29 pages
http://dx.doi.org/10.1155/IJMMS/2006/78192

Schrödinger equations in noncylindrical domains: exact controllability

1Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rio de Janeiro 20550-900, Brazil
2Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-590, Brazil
3Instituto de Matemática, Universidade Federal Fluminense, Rio de Janeiro 24020-140, Niterói, Brazil

Received 6 July 2005; Accepted 12 March 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider an open bounded set Ωn and a family {K(t)}t0 of orthogonal matrices of n. Set Ωt={xn;x=K(t)y,for all yΩ}, whose boundary is Γt. We denote by Q^ the noncylindrical domain given by Q^=0<t<T{Ωt×{t}}, with the regular lateral boundary Σ^=0<t<T{Γt×{t}}. In this paper we investigate the boundary exact controllability for the linear Schrödinger equation uiΔu=f in Q^(i2=1), u=w on Σ^, u(x,0)=u0(x) in Ω0, where w is the control.