Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source

Fan Yang, Ping Fan, Xiao-Xiao Li and Xin-Yi Ma
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Fan Yang: School of Science, Lanzhou University of Technology, Lanzhou 730050, China
Ping Fan: School of Science, Lanzhou University of Technology, Lanzhou 730050, China
Xiao-Xiao Li: School of Science, Lanzhou University of Technology, Lanzhou 730050, China
Xin-Yi Ma: School of Science, Lanzhou University of Technology, Lanzhou 730050, China

Mathematics, 2019, vol. 7, issue 9, 1-13

Abstract: In present paper, we deal with a backward diffusion problem for a time-fractional diffusion problem with a nonlinear source in a strip domain. We all know this nonlinear problem is severely ill-posed, i.e., the solution does not depend continuously on the measurable data. Therefore, we use the Fourier truncation regularization method to solve this problem. Under an a priori hypothesis and an a priori regularization parameter selection rule, we obtain the convergence error estimates between the regular solution and the exact solution at 0 ≤ x < 1 .

Keywords: time-fractional diffusion problem; ill-posed problem; Fourier truncation method; error estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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