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On the time periodic thermistor problem

Published online by Cambridge University Press:  14 April 2004

WALTER ALLEGRETTO ,
YANPING LIN  and
SHUQING MA
WALTER ALLEGRETTO
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton AB, Canada T6G 2G1 email: retl@retl.math.ualberta.ca
YANPING LIN
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton AB, Canada T6G 2G1 email: ylin@retl.math.ualberta.ca
SHUQING MA
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton AB, Canada T6G 2G1 email: ma@retl.math.ualberta.ca
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Abstract

In this paper we study a nonlocal parabolic/elliptic system which models thermistor behaviour in cases where heat losses to the surrounding gas play a significant role. The existence of time periodic solutions for the system is established through Faedo-Galerkin approximations and the Leray–Schauder degree theory. We show that for the small gas pressure case, the temperature of the time periodic solutions is positive. Moreover we consider the long time behaviour of the system and prove the existence of a uniform attractor. Finally, the finite dimensionality of the attractor is discussed.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 15 , Issue 1 , February 2004 , pp. 55 - 77
Copyright
© 2004 Cambridge University Press

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