A Carleman estimate for infinite cylindrical quantum domains and the application to inverse problems

被引：21
作者：
Kian, Yavar [1 ,2 ]
Phan, Quang Sang [3 ]
Soccorsi, Eric [1 ,2 ]
机构：
[1] Univ Aix Marseille, CPT, CNRS, UMR 7332, F-13288 Marseille, France
[2] Univ Toulon & Var, F-83957 La Garde, France
[3] Jagiellonian Univ, Inst Math, Fac Math & Comp Sci, PL-30348 Krakow, Poland
来源：
INVERSE PROBLEMS | 2014年 / 30卷 / 05期
关键词：
inverse problem; Schrodinger equation; Carleman estimate; scalar potential; infinite cylindrical domain; LIPSCHITZ STABILITY; UNIQUENESS; COEFFICIENTS; EQUATIONS;
D O I：
10.1088/0266-5611/30/5/055016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the inverse problem of determining the time-independent scalar potential q of the dynamic Schrodinger equation in an infinite cylindrical domain Omega, from one Neumann boundary observation of the solution. Assuming that q is known outside some fixed compact subset of Omega, we prove that q may be Lipschitz stably retrieved by choosing the Dirichlet boundary condition of the system suitably. Since the proof is by means of a global Carleman estimate designed specifically for the Schrodinger operator acting in an unbounded cylindrical domain, the measurement of the Neumann data is performed on an infinitely extended subboundary of the cylinder.
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页数：16
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