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

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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>0</mn> <mo>&#8804;</mo> <mi>x</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>.

# Mathematics # time-fractional diffusion problem # ill-posed problem # Fourier truncation method # error estimate

Fan Yang, Ping Fan, Xiao-Xiao Li, et al. (2019). "Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source". Mathematics. https://doi.org/10.3390/math7090865