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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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