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Initial temperature reconstruction for a nonlinear heat equation

Application to radiative heat transfer
: Pereverzyev, S.; Pinnau, R.; Siedow, N.

Volltext (PDF; )

Lesnic, D.:
5th International Conference on Inverse Problems in Engineering : Theory and practice. Vol. 3. Held at the University of Cambridge, Clare College, 11 - 15 July 2005
Leeds: Leeds University Press, 2005
ISBN: 0-85316-24-2
Ch. P02, S.1-8
International Conference on Inverse Problems in Engineering "Theory and Practice" <5, 2005, Cambridge>
Konferenzbeitrag, Elektronische Publikation
Fraunhofer ITWM ()

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