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Initial temperature reconstruction for nonlinear heat equation: Application to a coupled radiative-conductive heat transfer problem

: Pereverzyev, S.S.; Pinnau, R.; Siedow, N.


Inverse problems in science and engineering 16 (2008), Nr.1, S.55-67
ISSN: 1741-5977
ISSN: 1741-5985
International Conference on Inverse Problems in Engineering "Theory and Practice" <5, 2005, Cambridge>
Zeitschriftenaufsatz, Konferenzbeitrag
Fraunhofer ITWM ()

In a cooling process described by a nonlinear heat equation, we are interested to recover the initial temperature from the temperature measurements that are available on a part of the boundary for some time. Up to now, even for the linear heat equation, this problem usually has been studied as a nonlinear ill-posed operator equation, and regularization methods involving Frchet derivatives have been applied. We propose a fast derivative-free iterative method. Numerical results are presented for the glass cooling process where the nonlinearity appears due to radiation.