Title: Determining the temperature from Cauchy data in corner domains

Authors: B. Tomas Johansson

Addresses: School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

Abstract: We consider the problem of reconstruction of the temperature from knowledge of the temperature and heat flux on a part of the boundary of a bounded planar domain containing corner points. An iterative method is proposed involving the solution of mixed boundary value problems for the heat equation (with time-dependent conductivity). These mixed problems are shown to be well-posed in a weighted Sobolev space.

Keywords: Cauchy problem; corner domains; heat equations; ill-posed; iterative regularisation; weighted Sobolev space; temperature reconstruction; heat flux; mixed boundary value; time-dependent conductivity.

DOI: 10.1504/IJCSM.2010.033930

International Journal of Computing Science and Mathematics, 2010 Vol.3 No.1/2, pp.122 - 131

Published online: 04 Jul 2010 *

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