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Regularity of weak solution for a coupled system arising from a microwave heating model

Published online by Cambridge University Press:  02 September 2013

HONG-MING YIN  and
WEI WEI
HONG-MING YIN*
Affiliation:
Department of Mathematics, Washington State University, Pullman, WA 99164, USA email: hyin@wsu.edu
WEI WEI
Affiliation:
Department of Mathematics, Guizhou University, Guiyang, Guizhou Province, China email: wwei@gzu.edu.cn
*
†Corresponding author.
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Abstract

In this paper, we study the regularity of a weak solution for a coupled system derived from a microwave-heating model. The main feature of this model is that electric conductivity in the electromagnetic field is assumed to be temperature dependent. It is shown that the weak solution of the coupled system possesses some regularity under certain conditions. In particular, it is shown that the temperature is Hölder continuous, even if electric conductivity has a jump discontinuity with respect to the temperature change. The main idea in the proof is based on an estimate for a linear degenerate system in Campanato space. As an application, the regularity result for the coupled system is used to derive the necessary condition for an optimal control problem arising in microwave heating processes.

Keywords

Time-harmonic Maxwell's systemTemperature-dependent electric conductivityMicrowave heating modelRegularity of weak solutions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 1 , February 2014 , pp. 117 - 131
Copyright
Copyright © Cambridge University Press 2013 

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