On an inverse source problem for the heat equation. Application to a pollution detection problem. II. (English) Zbl 1326.65121

Summary: 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.


65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
86A22 Inverse problems in geophysics
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