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Inverse problem of time-dependent heat sources numerical reconstruction. (English) Zbl 1219.65103
Authors’ abstract: We study the inverse problem of reconstructing a time-dependent heat source in the heat conduction equation using the temperature measurement specified at an internal point. Problems of this type have important applications in several fields of applied science. By the Green function method, the inverse problem is reduced to an operator equation of the first kind which is known to be ill-posed. The uniqueness of the solution for the inverse problem is obtained by the contraction mapping principle. A numerical algorithm on the basis of the Landweber iteration is designed to deal with the operator equation and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown heat source is recovered very well.

MSC:
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R30 Inverse problems for PDEs
65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
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