Coupled linear Schrödinger equations: Control and stabilization results

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00585946" target="_blank" >RIV/67985840:_____/24:00585946 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00033-024-02242-7" target="_blank" >https://doi.org/10.1007/s00033-024-02242-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00033-024-02242-7" target="_blank" >10.1007/s00033-024-02242-7</a>

Result language
angličtina
Original language name
Coupled linear Schrödinger equations: Control and stabilization results
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GC22-08633J" target="_blank" >GC22-08633J: Qualitative Theory of the MHD and Related Equations</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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