A New Carleman Inequality for a Linear Schrödinger Equation on Some Unbounded Domains

This article presents a new Carleman inequality for a linear Schrödinger equation which is suitable for both bounded and unbounded domains. We characterize the conditions on the auxiliary function necessary to obtain the global inequality. The novelty of this result is the construction of the auxili...

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Bibliographic Details
Published in:Applied mathematics & optimization 2023-02, Vol.87 (1), p.8, Article 8
Main Authors: de la Vega, Constanza Sánchez F., de Teresa, Luz, Torres, Pablo
Format: Article
Language:English
Subjects:
Applied mathematics
Calculus of Variations and Optimal Control
Optimization
Control
Domains
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Schrodinger equation
Simulation
Systems Theory
Theoretical
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Summary:This article presents a new Carleman inequality for a linear Schrödinger equation which is suitable for both bounded and unbounded domains. We characterize the conditions on the auxiliary function necessary to obtain the global inequality. The novelty of this result is the construction of the auxiliary function on some unbounded domains and for a corresponding valid control region ω . As a consequence, we prove some results on the controllability of a linear Schrödinger equation on unbounded domains.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-022-09922-8