On the time periodic thermistor problem

Walter Allegretto, Yanping Lin, Shuqing Ma

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6 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)55-77
Number of pages23
JournalEuropean Journal of Applied Mathematics
Volume15
Issue number1
DOIs
Publication statusPublished - 1 Feb 2004
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics

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