Recovering a time-dependent potential function in a multi-term time fractional diffusion equation by using a nonlinear condition-Reference-Cited by-同舟云学术

Recovering a time-dependent potential function in a multi-term time fractional diffusion equation by using a nonlinear condition

Published:2020-09-29 Issue:2 Volume:29 Page:233-248
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Jiang Su Zhen¹^ORCID,Wu Yu Jiang¹^ORCID

Affiliation:

1. School of Mathematics and Statistics , Lanzhou University , Gansu 730000 , P. R. China

Abstract

Abstract In the present paper, we devote our effort to a nonlinear inverse problem for recovering a time-dependent potential term in a multi-term time fractional diffusion equation from an additional measurement in the form of an integral over the space domain. First we study the existence, uniqueness, regularity and stability of the solution for the direct problem by using the fixed point theorem. And we obtain the uniqueness of the inverse time-dependent potential term problem. Numerically, we use the Levenberg–Marquardt method to find the approximate potential function. Four different examples are presented to show the feasibility and efficiency of the proposed method.

Funder

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2019-0055/pdf

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