Determining the temperature from incomplete boundary data

✍ Scribed by B. Tomas Johansson

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 226 KB
• Volume: 280
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200610577

✦ Synopsis

Abstract

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well‐posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L^2^‐space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)