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

Abstract

Abstract - We consider the problem of identification of a heat source in a bounded domain Ω. 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 Γ 0 × (0 , T ), where Γ 0 is a part of the boundary of Ω, with non void interior, and T > T∗ . By a standard trandformation, we derive from these results a method to identify the polluting sources on the surface of a river, a lake . . .