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

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.

Automated summary

This study investigates the inverse and ill-posed problem of determining solute concentration for a two-dimensional nonhomogeneous fractional diffusion equation. The model becomes more complex with the presence of a source term. We propose a modified kernel regularization technique for stable numerical reconstruction of the solution, and provide convergence estimates under both a priori and a posteriori parameter choice rules.