A mollified method for the solution of the Cauchy problem for the convection–diffusion equation

@article{Lesnic2007AMM,
title={A mollified method for the solution of the Cauchy problem for the convection–diffusion equation},
author={D. Lesnic and G. Wake},
journal={Inverse Problems in Science and Engineering},
year={2007},
volume={15},
pages={293 - 302}
}

The inverse problem that requires finding the upstream flow of a diffusion column from measurements of the flow at the bottom of the column is investigated. The problem is mathematically formulated as a Cauchy problem for the convection–diffusion equation. The solution is sought using a mollification method which filters the input measured data prior to inversion. Although the original Cauchy problem is ill-posed, the mollified problem is proved to be well-posed and stability estimates are… Expand