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.
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