Uniqueness for time-dependent inverse problems with single dynamical data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:497

Article

Ben Aicha, Ibtissem¹  Hu, Guang-Hui^2,3  Vashisth, Manmohan⁴  Zou, Jun⁵ 

[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[4] Indian Inst Technol, Dept Math, Jammu 181221, India

[5] Chinese Univ Hong Kong, Dept Math, Hong Kong, Peoples R China

关键词: Wave equation;    Schrodinger equation;    Inverse problem;    Single measurement;    Shape identification;    Coefficient determination;   

DOI  :  10.1016/j.jmaa.2020.124910

来源: Elsevier

【 摘 要 】

In this work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal obstacle and the coefficient appearing in the wave and Schrodinger equations from a single dynamical data. With the near-field data, we first prove that the sound speed of the wave equation together with its contrast support of convex-polygon type can be uniquely determined, then establish a uniqueness result for recovering an electric potential as well as its support appearing in the Schrodinger equation. As a consequence of these results, we demonstrate a uniqueness result for recovering the refractive index of a medium from a single far field pattern at a fixed frequency in the time-harmonic regime. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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