LIPSCHITZ STABILITY IN INVERSE SOURCE AND INVERSE COEFFICIENT PROBLEMS FOR A FIRST- AND HALF-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

被引：3

作者：

Kawamoto, Atsushi ^{[1
]}

Machida, Manabu ^{[2
]}

机构：

[1] Univ Tokyo, Dept Math Sci, Meguro Ku, Tokyo 1538914, Japan

[2] Hamamatsu Univ Sch Med, Inst Med Photon Res, Hamamatsu, Shizuoka 4313192, Japan

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2020年 / 52卷 / 01期

基金：

日本学术振兴会;

关键词：

fractional diffusion equation; inverse problem; Carleman estimate; stability estimate; UNIQUENESS; FLOW;

D O I：

10.1137/18M1235776

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider inverse problems for the first- and half-order time-fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates.

引用

页码：967 / 1005

页数：39

共 50 条

[1] Lipschitz stability estimates in inverse source problems for a fractional diffusion equation of half order in time by Carleman estimates
Kawamoto, Atsushi
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2018, 26 (05): : 647 - 672
[2] INVERSE PROBLEMS FOR A HALF-ORDER TIME-FRACTIONAL DIFFUSION EQUATION IN ARBITRARY DIMENSION BY CARLEMAN ESTIMATES
Huang, Xinchi
Kawamoto, Atsushi
INVERSE PROBLEMS AND IMAGING, 2022, 16 (01) : 39 - 67
[3] HOLDER STABILITY ESTIMATE IN AN INVERSE SOURCE PROBLEM FOR A FIRST AND HALF ORDER TIME FRACTIONAL DIFFUSION EQUATION
Kawamoto, Atsushi
INVERSE PROBLEMS AND IMAGING, 2018, 12 (02) : 315 - 330
[4] An inverse coefficient-source problem for a time-fractional diffusion equation
Settara, Loubna
Atmania, Rahima
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2018, 57 (03): : 68 - 78
[5] An inverse source problem for distributed order time-fractional diffusion equation
Sun, Chunlong
Liu, Jijun
INVERSE PROBLEMS, 2020, 36 (05)
[6] Conditional stability and regularization method for inverse source for distributed order time-fractional diffusion equation
Chen, Yongbo
Cheng, Hao
COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (07)
[7] Conditional stability for an inverse coefficient problem of a weakly coupled time-fractional diffusion system with half order by Carleman estimate
Ren, Caixuan
Huang, Xinchi
Yamamoto, Masahiro
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2021, 29 (05): : 635 - 651
[8] An inverse source problem in a semilinear time-fractional diffusion equation
Slodicka, M.
Siskova, K.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (06) : 1655 - 1669
[9] Inverse coefficient problem for the time-fractional diffusion equation with Hilfer operator
Durdiev, D. K.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (16) : 17469 - 17484
[10] Inverse Coefficient Problem for a Time-Fractional Diffusion Equation in the Bounded Domain
D. K. Durdiev
J. J. Jumaev
Lobachevskii Journal of Mathematics, 2023, 44 : 548 - 557

← 1 2 3 4 5 →