DETERMINATION OF A SOURCE TERM IN SCHRO<spacing diaeresis>DINGER EQUATION WITH DATA TAKEN AT FINAL MOMENT OF OBSERVATION

被引：3

作者：

Imanuvilov, Oleg ^{[1
]}

Yamamoto, Masahiro ^{[2
,3
,4
]}

机构：

[1] Colorado State Univ, Dept Math, 101 Weber Bldg, Ft Collins, CO 80523 USA

[2] Univ Tokyo, Grad Sch Math Sci, Meguro, Tokyo 1538914, Japan

[3] Acad Romanian Scientists, Ilfov 3, Bucharest, Romania

[4] Acad Peloritana Pericolanti, Messina, Italy

来源：

COMMUNICATIONS ON ANALYSIS AND COMPUTATION | 2024年 / 2卷 / 04期

关键词：

Schro<spacing diaeresis>diner equation; inverse problems; Carleman estimate; uniqueness; stability; LIPSCHITZ STABILITY; INVERSE PROBLEM; UNIQUENESS;

D O I：

10.3934/cac.2024016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish Lipschitz stability estimates in the inverse problems of determining a real-valued source term or a real-valued potential of a Schro<spacing diaeresis>dinger equation with time-dependent coefficients under some geometric assumption on observation subboundary. The arguments are based on a Carleman estimate with the weight which decays at t = 0.

引用

页码：316 / 342

页数：27

共 17 条

[1] Uniqueness and stability in an inverse problem for the Schrodinger equation (vol 18, pg 1537, 2002) [J].

Baudouin, L. ;

Puel, J-P .

INVERSE PROBLEMS, 2007, 23 (03) :1327-1328

[2] Uniqueness and stability in an inverse problem for the Schrodinger equation [J].

Baudouin, L ;

Puel, JP .

INVERSE PROBLEMS, 2002, 18 (06) :1537-1554

[3] An inverse problem for Schrodinger equations with discontinuous main coefficient [J].

Baudouin, Lucie ;

Mercado, Alberto .

APPLICABLE ANALYSIS, 2008, 87 (10-11) :1145-1165

[4]

Beilina L., 2012, Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems, DOI DOI 10.1007/978-1-4419-7805-9

[5]

Bukhgeim A., 2000, Introduction to the Theory of Inverse Problems

[6]

BUKHGEIM AL, 1981, DOKL AKAD NAUK SSSR+, V260, P269

[7] CONTROLLABILITY OF PARABOLIC EQUATIONS [J].

EMANUILOV, OY .

SBORNIK MATHEMATICS, 1995, 186 (5-6) :879-900

[8]

Hormander L., 1976, LINEAR PARTIAL DIFFE

[9] Carleman estimate for the Schrodinger equation and application to magnetic inverse problems [J].

Huang, Xinchi ;

Kian, Yavar ;

Soccorsi, Eric ;

Yamamoto, Masahiro .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 474 (01) :116-142

[10] Sharp uniqueness and stability of solution for an inverse source problem for the Schrodinger equation [J].

Imanuvilov, O. Y. ;

Yamamoto, M. .

INVERSE PROBLEMS, 2023, 39 (10)

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