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

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