An inverse problem for space-fractional backward diffusion problem

作者：Zhao Jingjun^*; Liu Songshu; Liu Tao

来源：Mathematical Methods in the Applied Sciences, 2014, 37(8): 1147-1158.

DOI：10.1002/mma.2876

• inverse problems
• fractional backward diffusion problem
• ill-posed problems
• regularization method

In this paper, an inverse problem for space-fractional backward diffusion equation, which is highly ill-posed, is considered. This problem is obtained from the classical diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha is an element of (0,2]. We show that such a problem is severely ill-posed, and further present a simplified Tikhonov regularization method to deal with this problem. Convergence estimate is presented under a priori choice of regularization parameter. Numerical experiments are given to illustrate the accuracy and efficiency of the proposed method.

• 出版日期2014-5-30
• 单位哈尔滨工业大学