Stabilization of the weakly coupled Schrödinger system

In this paper, we investigate the energy decay for solutions of the weakly coupled dissipative Schrödinger system. Among the m-coupled equations, only one equation is directly damped. Under some assumptions about the damping and the coupling terms, it is shown that sufficiently smooth solutions of t...

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Bibliographic Details
Published inApplicable analysis Vol. 101; no. 2; pp. 733 - 746
Main Authors Fu, Xiaoyu, Zhang, Hualei, Zhu, Xianzheng
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 22.01.2022
Taylor & Francis Ltd
Subjects
Boundary conditions
Carleman estimates
Coupled Schrödinger system
Coupling
Damping
Decay
Dirichlet problem
Interpolation
interpolation inequality
logarithmic decay
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ISSN0003-6811
1563-504X
DOI10.1080/00036811.2020.1758309

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Summary:In this paper, we investigate the energy decay for solutions of the weakly coupled dissipative Schrödinger system. Among the m-coupled equations, only one equation is directly damped. Under some assumptions about the damping and the coupling terms, it is shown that sufficiently smooth solutions of the system decay logarithmically with mixed boundary conditions, including the coupling of the Schrödinger system subject to Dirichlet and Robin type boundary conditions, respectively. The proof is based on some frequency estimates with an exponential loss on the resolvent operators, which will be solved by establishing an interpolation inequality for a suitable weakly coupled elliptic system.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2020.1758309