Initial Temperature Reconstruction for a Nonlinear Heat Equation: Application to Radiative Heat Transfer

  • 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.

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Author:Sergiy Pereverzyev, Rene Pinnau, Norbert Siedow
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (261)
Document Type:Preprint
Language of publication:English
Year of Completion:2005
Year of Publication:2005
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2005/02/04
Tag:initial temperature reconstruction; inverse problem; numerics; radiative heat transfer
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011