Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data. (23rd October 2020)

• Record Type: Journal Article
• Authors: Li, Zhiyuan; Zhang, Zhidong
• Is Part Of: Inverse problems. Volume 36:Number 11(2020)
• Publication Date: 2020-10-23
• Subjects: fractional diffusion equation -- inverse problem -- nonlinearity -- sparse measurements -- uniqueness -- multiple unknowns; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abbc5d
• Languages: English
• ISSNs: 0266-5611

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.