Inverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates

Xinchi Huang; Atsushi Kawamoto

doi:10.3934/ipi.2021040

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2022, Volume 16, Issue 1: 39-67. Doi: 10.3934/ipi.2021040

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Inverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates

Xinchi Huang^1, , and
Atsushi Kawamoto^2,

1.
Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan
2.
Department of Liberal Arts and Sciences, Faculty of Engineering, Takushoku University, Tatemachi, Hachioji, Tokyo, 193-0985, Japan

^* Corresponding author: Xinchi Huang
^* Corresponding author: Xinchi Huang

Received: September 30, 2020

Revised: February 28, 2021

Early access: May 2021

Published: February 2022

The first author is supported by Japan Society for the Promotion of Science under the program of JSPS Postdoctoral Fellowships for Research in Japan

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Abstract

We consider a half-order time-fractional diffusion equation in arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some additional assumptions. We establish the stability estimate of Lipschitz type in the inverse problems and the proofs are based on the Bukhgeim-Klibanov method by using Carleman estimates.

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Mathematics Subject Classification: Primary: 35R11, 35R30; Secondary: 35G05.

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