An inverse problem for fractional diffusion equation in 2-dimensional case: Stability analysis and regularization

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:393

Article

Xiong, Xiangtuan¹  Zhou, Qian¹  Hon, Y. C.² 

[1] NW Normal Univ, Dept Math, Lanzhou, Gansu, Peoples R China

[2] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

关键词: Time-fractional diffusion equation;    Ill-posedness;    Stability estimate;    Regularization;    Numerical approximation;   

DOI  :  10.1016/j.jmaa.2012.03.013

来源: Elsevier

【 摘 要 】

In this paper we investigate an inverse problem for a time-fractional diffusion equation which is highly ill-posed in the two-dimensional setting. Based on an a priori assumption, we give a conditional stability result. Some new regularization methods are constructed for solving the inverse problem and the corresponding error estimates are proved. For numerical illustration, several examples are constructed to demonstrate the feasibility and efficiency of the proposed methods. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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