Entropy production as a regularization factor in solving an inverse diffusion problem

Abstract

Inverse diffusion problems allow the diffusion coefficients to be determined from experimental concentration profiles. Solutions of the inverse diffusion problem are unstable toward perturbations of the initial concentration profiles. By the example of inverse diffusion problem solution for a model binary system it is demonstrated that the use of the production entropy to minimize the discrepancy functional stabilizes the solution even for significant perturbations of the initial concentration profile. The choice of the entropy production for the smoothing component of the discrepancy functional is physically adequate to the formulated problem, and the entropy production can be used to solve inverse problems of heat and mass transfer.