Recovering a time-dependent potential function in a time fractional diffusion equation by using a nonlinear condition. Issue 2 (1st February 2021)

• Record Type: Journal Article
• Authors: Jiang, Suzhen; Wei, Ting
• Is Part Of: Inverse problems in science and engineering. Volume 29:Issue 2(2021)
• Page Start: 174
• Page End: 195
• Publication Date: 2021-02-01
• Subjects: Fractional diffusion equation -- inverse problem time-dependent potential term -- uniqueness -- Levenberg–Marquardt method -- numerical example.; Inverse Problems; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2020.1782399
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : In this paper, we deal with a nonlinear inverse problem for recovering a time-dependent potential term in a time fractional diffusion equation from an additional measurement in the form of integral over the space domain. By using the fixed point theorem, the existence, uniqueness, regularity and stability of the direct problem are proved. The uniqueness of the inverse problem is proved by the property of Caputo fractional derivative. Numerically, we employ the Levenberg–Marquardt method to find the approximate potential function. Some different type examples are presented to show the feasibility and efficiency of the proposed method.