Coupled linear Schrödinger equations: Control and stabilization results
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911805141417984 |
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| author | Bhandari, K. Capistrano-Filho, R. de A. Majumdar, S. Tanaka, T. Y. |
| author_facet | Bhandari, K. Capistrano-Filho, R. de A. Majumdar, S. Tanaka, T. Y. |
| contents | This article presents some controllability and stabilization results for a system of two coupled linear Schrödinger equations in the one-dimensional case where the state components are interacting through the Kirchhoff boundary conditions. Considering the system in a bounded domain, the null boundary controllability result is shown. The result is achieved thanks to a new Carleman estimate, which ensures a boundary observation. Additionally, this boundary observation together with some trace estimates, helps us to use the Gramian approach, with a suitable choice of feedback law, to prove that the system under consideration decays exponentially to zero at least as fast as the function $e^{-2ωt}$ for some $ω>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04931 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Coupled linear Schrödinger equations: Control and stabilization results Bhandari, K. Capistrano-Filho, R. de A. Majumdar, S. Tanaka, T. Y. Analysis of PDEs Optimization and Control 35K20, 35Q55, 93B05, 93B07, 93B52 This article presents some controllability and stabilization results for a system of two coupled linear Schrödinger equations in the one-dimensional case where the state components are interacting through the Kirchhoff boundary conditions. Considering the system in a bounded domain, the null boundary controllability result is shown. The result is achieved thanks to a new Carleman estimate, which ensures a boundary observation. Additionally, this boundary observation together with some trace estimates, helps us to use the Gramian approach, with a suitable choice of feedback law, to prove that the system under consideration decays exponentially to zero at least as fast as the function $e^{-2ωt}$ for some $ω>0$. |
| title | Coupled linear Schrödinger equations: Control and stabilization results |
| topic | Analysis of PDEs Optimization and Control 35K20, 35Q55, 93B05, 93B07, 93B52 |
| url | https://arxiv.org/abs/2310.04931 |