On the exact controllability of hyperbolic magnetic Schrödinger equations
In this paper, we address the exact controllability problem for the hyperbolic magnetic Schrödinger equation, which plays an important role in the research of electromagnetics. Typical techniques, such as Hamiltonian induced Hilbert spaces and pseudodifferential operators are introduced. By choosin...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Basque Center for Applied Mathematics (BCAM) |
| Repositório: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/200 |
| Acesso em linha: | http://hdl.handle.net/20.500.11824/200 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Observability Compactness-uniqueness argument Energy conservation law Hamiltonian operators Hilbert uniqueness method Observability inequality Pseudo-differential operator Trace theorem Unique continuation Mathematical operators |
| Resumo: | In this paper, we address the exact controllability problem for the hyperbolic magnetic Schrödinger equation, which plays an important role in the research of electromagnetics. Typical techniques, such as Hamiltonian induced Hilbert spaces and pseudodifferential operators are introduced. By choosing an appropriate multiplier, we proved the observability inequality with sharp constants. In particular, a genuine compactness-uniqueness argument is applied to obtain the minimal time. In the final analysis, a suitable boundary control is constructed by the systematic Hilbert Uniqueness Method introduced by J. L. Lions. Compared with the micro-local discussion in Bardos et al. (1992), we do not require the coefficients belong to C∞. Actually, C1 is already sufficient for the vector potential of the hyperbolic electromagnetic equation. |
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