Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation

Yonggang Chen, Yu Qiao and Xiangtuan Xiong
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Yonggang Chen: College of Science, China University of Petroleun East China, Qingdao 257099, China
Yu Qiao: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Xiangtuan Xiong: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2022, vol. 10, issue 10, 1-14

Abstract: The inverse and ill-posed problem of determining a solute concentration for the two-dimensional nonhomogeneous fractional diffusion equation is investigated. This model is much worse than its homogeneous counterpart as the source term appears. We propose a modified kernel regularization technique for the stable numerical reconstruction of the solution. The convergence estimates under both a priori and a posteriori parameter choice rules are proven.

Keywords: sideways problem; nonhomogeneous fractional diffusion equation; ill-posedness; error estimates; regularization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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