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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.

MSC:

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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