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Identification of the time-dependent source term in a multi-term time-fractional diffusion equation

  • Y. S. Li
  • L. L. Sun
  • Z. Q. Zhang
  • T. WeiEmail author
Original Paper
  • 13 Downloads

Abstract

The multi-term time-fractional diffusion equation is a useful tool in the modeling of complex systems. This paper aims to identifying a time-dependent source term in a multi-term time-fractional diffusion equation from the boundary Cauchy data. The regularity of the weak solution for the direct problem with homogeneous Neumann boundary condition is proved. We provide the uniqueness and a stability estimate for the inverse time-dependent source problem. On the other hand, the inverse time-dependent source term is formulated into a variational problem by the Tikhonov regularization, with the help of sensitivity problem and adjoint problem we use a conjugate gradient method to find the approximate time-dependent source term. Numerical experiments for five examples in one-dimensional and two-dimensional cases show that our proposed method is effective and stable.

Keywords

Inverse source problem Multi-term time-fractional diffusion equation Conjugate gradient method 

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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityGansuPeople’s Republic of China
  2. 2.School of Cyber SecurityGansu Institute of Political Science and LawLanzhouPeople’s Republic of China

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