Open AccessInverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates
Author(s) -
Xinchi Huang,
Atsushi Kawamoto
Publication year - 2022
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021040
Subject(s) - lipschitz continuity , dimension (graph theory) , mathematics , inverse , inverse problem , diffusion , diffusion equation , mathematical proof , stability (learning theory) , order (exchange) , term (time) , mathematical analysis , computer science , pure mathematics , physics , geometry , economy , finance , quantum mechanics , machine learning , economics , thermodynamics , service (business)
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.