Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data

2020/03/24 by Zhiyuan Li, Zhidong Zhang · 25 citations
Mathematics · #Boundary (topology) #Differential Equations and Boundary Problems #Fractional Differential Equations Solutions #Inverse #Inverse problem #Laplace transform #Numerical methods in inverse problems #Order (exchange) #Sequence (biology) #Term (time) #Uniqueness #math.AP #msc:26A33 #msc:35R11 #msc:35R30

paper · pdf · doi:10.1088/1361-6420/abbc5d

published in Inverse Problems 36(11), 115013 (IOP Publishing)

arxiv created 2020/03/24 · openalex created_date 2020/04/03 · openalex publication_date 2020/09/28 · arxiv updated 2020/12/02 · openalex updated_date 2026/08/05

Abstract

Abstract In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By using a sequence of harmonic functions, we construct useful quantitative relation between the unknowns and measurements. From Laplace transform and the knowledge in complex analysis, the uniqueness theorem is proved.

Citations

• Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins
• Hitchhikerʼs guide to the fractional Sobolev spaces
• Application of a fractional advection‐dispersion equation
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations