Hölder continuous solutions of an obstacle thermistor problem
Walter Allegretto - Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB, Canada T6G 2G1, Canada (email)
Abstract: 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: Obstacle thermistor problem, current driven, existence, uniqueness.
Received: March 2003; Revised: April 2004; Published: August 2004.
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