On an inverse source problem for the heat equation. Application to a pollution detection problem.(English)Zbl 1028.35164

Summary: We consider the problem of identification of a heat source in a bounded domain $$\Omega$$. Assuming that the point sources became inactive after the time $$T_*$$, we prove that they can be identified by measurements of the heat flux on $$\Gamma_0\times(0, T)$$, where $$\Gamma_0$$ is a part of the boundary of $$\Omega$$, with non-void interior, and $$T> T_*$$. By a standard transformation, we derive from these results a method to identify the polluting sources on the surface of a river, a lake.

MSC:

 35R30 Inverse problems for PDEs 35K05 Heat equation 80A23 Inverse problems in thermodynamics and heat transfer
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