Simultaneous uniqueness for an inverse problem in a time-fractional diffusion equation

被引：14

作者：

Jing, Xiaohua ^{[1
]}

Peng, Jigen ^{[2
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

[2] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2020年 / 109卷

基金：

中国国家自然科学基金;

关键词：

Determination of fractional-order; Inverse potential problem; Robin inverse problem; Time fractional diffusion equation;

D O I：

10.1016/j.aml.2020.106558

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article investigates the uniqueness of identifying the fractional-order, potential, and Robin coefficient simultaneously in one-dimensional time-fractional diffusion equation with non-homogeneous boundary condition. By using one boundary measurement, we prove that the fractional-order, potential on the entire interval, and Robin coefficient are determined simultaneously from asymptotic properties of the Mittag-Leffler function and the Marchenko's uniqueness theorem. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：7

共 11 条

[1] Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation [J].

Cheng, Jin ;

Nakagawa, Junichi ;

Yamamoto, Masahiro ;

Yamazaki, Tomohiro .

INVERSE PROBLEMS, 2009, 25 (11)

[2]

Freiling G., 2001, Inverse Sturm-Liouville problems and their applications

[3] FRACTIONAL DIFFUSION EQUATION AND RELAXATION IN COMPLEX VISCOELASTIC MATERIALS [J].

GIONA, M ;

CERBELLI, S ;

ROMAN, HE .

PHYSICA A, 1992, 191 (1-4) :449-453

[4]

Kirsch A, 2011, APPL MATH SCI, V120, P1, DOI 10.1007/978-1-4419-8474-6

[5] Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation [J].

Li, Gongsheng ;

Zhang, Dali ;

Jia, Xianzheng ;

Yamamoto, Masahiro .

INVERSE PROBLEMS, 2013, 29 (06)

[6] Uniqueness in inverse boundary value problems for fractional diffusion equations [J].

Li, Zhiyuan ;

Imanuvilov, Oleg Yu ;

Yamamoto, Masahiro .

INVERSE PROBLEMS, 2016, 32 (01)

[7] Coefficient inverse problem for a fractional diffusion equation [J].

Miller, Luc ;

Yamamoto, Masahiro .

INVERSE PROBLEMS, 2013, 29 (07)

[8]

Podlubny I., 2013, MATH SCI ENG, V2013, P553

[9] Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems [J].

Sakamoto, Kenichi ;

Yamamoto, Masahiro .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 382 (01) :426-447

[10] Identification of the zeroth-order coefficient in a time fractional diffusion equation [J].

Sun, Liangliang ;

Wei, Ting .

APPLIED NUMERICAL MATHEMATICS, 2017, 111 :160-180

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