Articles

THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION

  • Fan YANG ,
  • Yan ZHANG ,
  • Xiao LIU ,
  • Xiaoxiao LI
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  • Department of Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

Received date: 2019-09-04

  Online published: 2020-07-17

Supported by

The project is supported by the National Natural Science Foundation of China (11561045, 11961044) and the Doctor Fund of Lan Zhou University of Technology.

Abstract

In this article, we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation. This problem is ill-posed and the quasi-boundary value method is proposed to deal with this inverse problem and obtain the series expression of the regularized solution for the inverse initial value problem. We prove the error estimates between the regularization solution and the exact solution by using an a priori regularization parameter and an a posteriori regularization parameter choice rule. Some numerical results in one-dimensional case and two-dimensional case show that our method is efficient and stable.

Cite this article

Fan YANG , Yan ZHANG , Xiao LIU , Xiaoxiao LI . THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION[J]. Acta mathematica scientia, Series B, 2020 , 40(3) : 641 -658 . DOI: 10.1007/s10473-020-0304-5

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