DCDS
Existence and long time behaviour of solutions to obstacle thermistor equations
Walter Allegretto Yanping Lin Shuqing Ma
Discrete & Continuous Dynamical Systems - A 2002, 8(3): 757-780 doi: 10.3934/dcds.2002.8.757
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.
DCDS-B
Hölder continuous solutions of an obstacle thermistor problem
Walter Allegretto Yanping Lin Shuqing Ma
Discrete & Continuous Dynamical Systems - B 2004, 4(4): 983-997 doi: 10.3934/dcdsb.2004.4.983
In this paper we consider a thermistor problem with a current source, i.e., a nonlocal boundary condition. The electric potential is unknown on part of the boundary, but the current through it is known. We apply a decomposition technique and transform the equation satisfied by the potential into two elliptic problems with usual boundary conditions. The unique solvability of the initial boundary value problem is achieved.
keywords: existence uniqueness. current driven Obstacle thermistor problem
DCDS-B
On the box method for a non-local parabolic variational inequality
Walter Allegretto Yanping Lin Shuqing Ma
Discrete & Continuous Dynamical Systems - B 2001, 1(1): 71-88 doi: 10.3934/dcdsb.2001.1.71
In this paper we study a box scheme (or finite volume element method) for a non-local nonlinear parabolic variational inequality arising in the study of thermistor problems. Under some assumptions on the data and regularity of the solution, optimal error estimates in the $H^1$-norm are attained.
keywords: Box methods non-local thermistor and variational inequality.

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