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

2020/10/20 by Xinchi Huang, Huang, X., Atsushi Kawamoto +1
Computer Science · Mathematics · #35R11 #35R30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2010.10082

openalex publication_date 2020/10/20 · openalex created_date 2020/10/29 · openalex updated_date 2026/07/28

Abstract

We consider a half-order time-fractional diffusion equation in an 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.

Citations

• The random walk's guide to anomalous diffusion: a fractional dynamics approach

Related

• Lipschitz stability in inverse source and inverse coefficient problems for a first- and half-order time-fractional diffusion equation
• Hölder stability estimate in an inverse source problem for a first and half order time fractional diffusion equation
• Conditional stability for an inverse source problem for the time-fractional diffusion equation
• Determination of time dependent factors of coefficients in fractional diffusion equations
• Global Lipschitz stability for a fractional inverse transport problem by Carleman estimates