On the simultaneous reconstruction of boundary Robin coefficient and internal source in a slow diffusion system. (2nd July 2021)

• Record Type: Journal Article
• Authors: Zhang, Mengmeng; Liu, Jijun
• Is Part Of: Inverse problems. Volume 37:Number 7(2021)
• Publication Date: 2021-07-02
• Subjects: slow diffusion -- fractional order derivative -- uniqueness -- regularization -- error estimate -- numerics; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac0967
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Consider an inverse problem of simultaneous reconstruction of boundary impedance coefficient and space-dependent source term from the final measurement data for a slow diffusion system, which is governed by a diffusion equation with time-fractional order derivative and Robin boundary condition. We firstly prove the uniqueness of this inverse problem by the maximum principle for the slow diffusion system. Then a regularizing scheme combining the mollification method and the Tikhonov regularization is proposed to recover the two unknowns, with a rigorous analysis on the choice strategies for the regularizing parameters and the error estimates on the regularizing solutions, revealing the error propagation effects due to recovering the boundary Robin coefficient firstly. Numerical examples are presented to illustrate the validity of the proposed method and support our theoretical analysis.