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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/78192 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560608751386624 |
|---|---|
| author | G. O. Antunes M. D. G. da Silva R. F. Apolaya |
| author_facet | G. O. Antunes M. D. G. da Silva R. F. Apolaya |
| author_sort | G. O. Antunes |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-8f5c6db10da44ad5aeccf12128de53df |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8f5c6db10da44ad5aeccf12128de53df2025-02-03T01:27:13ZengWileyInternational 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 |
| 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 |
| title | 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_short | Schrödinger equations in noncylindrical domains: exact controllability |
| title_sort | schrodinger equations in noncylindrical domains exact controllability |
| url | http://dx.doi.org/10.1155/IJMMS/2006/78192 |
| work_keys_str_mv | AT goantunes schrodingerequationsinnoncylindricaldomainsexactcontrollability AT mdgdasilva schrodingerequationsinnoncylindricaldomainsexactcontrollability AT rfapolaya schrodingerequationsinnoncylindricaldomainsexactcontrollability |