Keywords:
Forschungsbericht
Description / Table of Contents:
Accurate modeling of heat transfer in high-temperatures situations requires to account for the effect of heat radiation. In complex applications such as Czochralski's method for crystal growth, in which the conduction radiation heat transfer problem couples to an induction heating problem and to the melt flow problem, we hardly can expect from the mathematical theory that the heat sources will be in a better space than L-1. In such situations, the known results on the unique solvability of the heat conduction problem with surface radiation do not apply, since a right-hand side in L-p with p 〈 6/5 no longer belongs to the dual of the Banach space in which coercivity is obtained. In this paper, we focus on a stationary heat equation with non-local boundary conditions and right-hand side in L-p with p〉=1 arbitrary. Essentially, we construct an approximation procedure and, thanks to new coercivity results, we are able to produce energy estimates that involve only the L-p-norm of the heat-sources, and to pass to the limit.
Type of Medium:
Online Resource
Pages:
Online-Ressource (39 S., 401 KB)
,
graph. Darst.
Series Statement:
Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 1240
URL:
http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2007/wias_preprints_1240.pdf
URL:
https://edocs.tib.eu/files/e01fn11/546267106.pdf
Language:
English
Note:
Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden
,
Systemvoraussetzungen: Acrobat reader.
Permalink