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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 2
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Articles

Stabilization of the weakly coupled Schrödinger system

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Pages 733-746 | Received 11 Nov 2019, Accepted 11 Apr 2020, Published online: 29 Apr 2020
 

ABSTRACT

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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Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the NSFC [grant number 11971333], [grant number 11931011].

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