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

doi:10.1007/s10473-020-0304-5

Abstract

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.

Key words: Space-time fractional diffusion equation, Ill-posed problem, quasi-boundary value method, identifying the initial value

CLC Number:

35R25

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.

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