Schrödinger equations in noncylindrical domains: exact controllability
We consider an open bounded set Ω⊂ℝn and a family {K(t)}t≥0 of orthogonal matrices of ℝn. Set Ωt={x∈ℝn;x=K(t)y,for all y∈Ω}, 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 i...
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Hindawi Limited
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/78192 |
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doaj-8f5c6db10da44ad5aeccf12128de53df2020-11-24T23:22:35ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/7819278192Schrödinger equations in noncylindrical domains: exact controllabilityG. O. Antunes0M. D. G. da Silva1R. F. Apolaya2Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rio de Janeiro 20550-900, BrazilInstituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-590, BrazilInstituto de Matemática, Universidade Federal Fluminense, Rio de Janeiro 24020-140, Niterói, BrazilWe consider an open bounded set Ω⊂ℝn and a family {K(t)}t≥0 of orthogonal matrices of ℝn. Set Ωt={x∈ℝn;x=K(t)y,for all y∈Ω}, 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 u′−iΔu=f in Q^(i2=−1), u=w on Σ^, u(x,0)=u0(x) in Ω0, where w is the control.http://dx.doi.org/10.1155/IJMMS/2006/78192 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
G. O. Antunes M. D. G. da Silva R. F. Apolaya |
| spellingShingle |
G. O. Antunes M. D. G. da Silva R. F. Apolaya Schrödinger equations in noncylindrical domains: exact controllability International Journal of Mathematics and Mathematical Sciences |
| author_facet |
G. O. Antunes M. D. G. da Silva R. F. Apolaya |
| author_sort |
G. O. Antunes |
| title |
Schrödinger equations in noncylindrical domains: exact controllability |
| title_short |
Schrödinger equations in noncylindrical domains: exact controllability |
| title_full |
Schrödinger equations in noncylindrical domains: exact controllability |
| title_fullStr |
Schrödinger equations in noncylindrical domains: exact controllability |
| title_full_unstemmed |
Schrödinger equations in noncylindrical domains: exact controllability |
| title_sort |
schrödinger equations in noncylindrical domains: exact controllability |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2006-01-01 |
| description |
We consider an open bounded set Ω⊂ℝn and a family {K(t)}t≥0 of orthogonal matrices of ℝn. Set Ωt={x∈ℝn;x=K(t)y,for all y∈Ω}, 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
u′−iΔu=f in Q^(i2=−1), u=w on Σ^, u(x,0)=u0(x) in Ω0, where w is the control. |
| url |
http://dx.doi.org/10.1155/IJMMS/2006/78192 |
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