Existence and long time behaviour of solutions to obstacle thermistor equations

Walter Allegretto; Yanping Lin; Shuqing Ma

doi:10.3934/dcds.2002.8.757

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2002, Volume 8, Issue 3: 757-780. Doi: 10.3934/dcds.2002.8.757

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Existence and long time behaviour of solutions to obstacle thermistor equations

1.
Department of Mathematical Sciences, University of Alberta, Edmonton A B, Canada T6G 2G1
2.
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1

Received: February 28, 2001

Revised: October 31, 2001

Published: June 2002

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Abstract

In this paper we introduce an obstacle thermistor system. The existence of weak solutions to the steady-state systems and capacity solutions to the time dependent systems are obtained by a penalized method under reasonable assumptions for the initial and boundary data. At the same time, we prove that there exists a uniform absorbing set for nonnegative initial data in $L_2(\Omega)$. Finally for smooth initial data a global attractor to the system is obtained by a series of Campanato space arguments.

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Mathematics Subject Classification: 35K55, 35R45.

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