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July  2002, 8(3): 757-780. doi: 10.3934/dcds.2002.8.757

Existence and long time behaviour of solutions to obstacle thermistor equations

Walter Allegretto 1, , Yanping Lin 2, and  Shuqing Ma 1,

1. 

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

Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Received  March 2001 Revised  November 2001 Published  April 2002

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.
Keywords: capacity solutions, Obstacle thermistor equations, global attractors..
Mathematics Subject Classification: 35K55, 35R4.
Citation: Walter Allegretto, Yanping Lin, Shuqing Ma. Existence and long time behaviour of solutions to obstacle thermistor equations. Discrete & Continuous Dynamical Systems, 2002, 8 (3) : 757-780. doi: 10.3934/dcds.2002.8.757
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