Schrödinger equations in noncylindrical domains: exact controllability

G. O. Antunes, M. D. G. da Silva and R. F. Apolaya

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-29

Abstract:

We consider an open bounded set Ω ⊂ ℝ n and a family { K ( t ) } t ≥ 0 of orthogonal matrices of ℝ n . Set Ω t = { x ∈ ℝ n ; x = K ( t ) y , for all y ∈ Ω } , whose boundary is Γ t . We denote by Q ^ the noncylindrical domain given by Q ^ = ∪ 0 < t < T { Ω t × { t } } , with the regular lateral boundary Σ ^ = ∪ 0 < t < T { Γ t × { t } } . In this paper we investigate the boundary exact controllability for the linear Schrödinger equation u ′ − i Δ u = f in Q ^ ( i 2 = − 1 ) , u = w on Σ ^ , u ( x , 0 ) = u 0 ( x ) in Ω 0 , where w is the control.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:078192

DOI: 10.1155/IJMMS/2006/78192

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