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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