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Source term identification in 1-D IHCP. (English) Zbl 1063.65102
Summary: We propose stable numerical solutions for the simultaneous identification of temperature, temperature gradient, and general source terms in the one-dimensional inverse heat conduction problem (IHCP).
The numerical solution consists of a regularization procedure, based on the mollification method, and a marching scheme for the solution of the stabilized problem. The stability, error analysis and implementation of the algorithm are presented together with a set of numerical results.

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
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
80A23 Inverse problems in thermodynamics and heat transfer
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
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