Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations. (24th March 2017)

• Record Type: Journal Article
• Authors: Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro
• Is Part Of: Inverse problems. Volume 33:Number 5(2017:May)
• Publication Date: 2017-03-24
• Subjects: fractional diffusion equation -- weak unique continuation -- inverse source problem -- iterative thresholding algorithm; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa58d1
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.