Source term identification in 1-D IHCP.

*(English)*Zbl 1063.65102Summary: 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 | Inverse problems (IVP of PDE, numerical methods) |

35K05 | Heat equation |

35R30 | Inverse problems for PDE |

65M06 | Finite difference methods (IVP of PDE) |

65M12 | Stability and convergence of numerical methods (IVP of PDE) |

65M15 | Error bounds (IVP of PDE) |

80A23 | Inverse problems (thermodynamics) |

80M20 | Finite difference methods (thermodynamics) |