A Backward Identification Problem for an Axis-Symmetric Fractional Diffusion Equation. Issue 3 (4th May 2017)

• Record Type: Journal Article
• Authors: Xiong, Xiangtuan; Ma, Xiaojun
• Is Part Of: Mathematical modelling and analysis. Volume 22:Issue 3(2017)
• Page Start: 311
• Page End: 320
• Publication Date: 2017-05-04
• Subjects: ill-posedness -- regularization -- fractional diffusion equation -- closed form solution; 65R35 -- 47A52; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2017.1309329
• Languages: English
• ISSNs: 1392-6292

Abstract

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.