A Backward Identification Problem for an Axis-Symmetric Fractional Diffusion Equation

Abstract

We consider a backward ill-posed problem for an axis-symmetric fractional diffusion equation which is described in polar coordinates. A closed form solution of the inverse problem is obtained. However, this solution blows up. For numerical stability, a general regularization principle is presented for constructing regularization methods. Several numerical examples are conducted for showing the validity and effectiveness of the proposed methods.

Keywords:

• ill-posedness
• regularization
• fractional diffusion equation
• closed form solution

AMS Subject Classification:

• 65R35
• 47A52