Identification of the Initial Value for a Time-Fractional Diffusion Equation

Author:

Yang Fan,Gao Yin-Xia,Li Dun-Gang,Li Xiao-Xiao

Abstract

In this manuscript, we study the inverse problem for identifying the initial value of a time-fractional diffusion equation in an axisymmetric region. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. We choose the Landweber iterative regularization method to solve this problem. Under the a priori and the a posteriori regularization parameter choice rules, we present the error estimates between the regularization solutions and the exact solution. We present some examples to show this method’s effectiveness.

Funder

the National Natural Science Foundation of China

the Natural Science Foundation of Gansu Province

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

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