Identifiability for a severely ill-posed oxygen balance model
Naïma Débit, Souad Khiari · Comptes Rendus Mathématique · 2016
We are interested in recovering boundary data in a dispersive oxygen-balance model. The missing boundary condition is the flux of the biochemical oxygen demand (the amount of oxygen necessary for the oxidation of organic matter) at one extreme point. The observations are collected on the dissolved oxygen at the other extremity. This problem turns out to be severely ill-posed. We perform the mathematical analysis of it. We prove a uniqueness result owing to Pazy's theorem for parabolic boundary value problems and we prove that the compatible data set is dense.