On an inverse source problem for the heat equation. Application to a pollution detection problem, II

Abstract

This work considers the inverse problem of localizing and characterizing multiple stationary pollution sources in surface waters or atmospheric media. This particular problem has been studied before and a uniqueness result was shown. In this paper, we revisit this work with the objective of providing a more complete study. In particular, an alternative uniqueness proof is conducted which is valid for more general pollution source structures. Additionally, a practical numerical identification method is developed and implemented. Finally, several numerical studies are performed which illustrate practical considerations as well as the effectiveness of the approach.