Hölder continuous solutions of an obstacle thermistor problem

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November 2004, 4(4): 983-997. doi: 10.3934/dcdsb.2004.4.983

Hölder continuous solutions of an obstacle thermistor problem

Walter Allegretto ^1, , Yanping Lin ^2, and Shuqing Ma ^3,

1.	Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB, Canada T6G 2G1, Canada
2.	Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
3.	Department of Mathematical Sciences, University of Alberta, Edmonton A B, Canada T6G 2G1

Received March 2003 Revised April 2004 Published August 2004

Abstract
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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.

Mathematics Subject Classification: 35R45, 49J4.

Citation: Walter Allegretto, Yanping Lin, Shuqing Ma. Hölder continuous solutions of an obstacle thermistor problem. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 983-997. doi: 10.3934/dcdsb.2004.4.983

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