Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Hölder continuous solutions of an obstacle thermistor problem

Pages: 983 - 997, Volume 4, Issue 4, November 2004      doi:10.3934/dcdsb.2004.4.983

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Walter Allegretto - Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB, Canada T6G 2G1, Canada (email)
Yanping Lin - Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1, Canada (email)
Shuqing Ma - Department of Mathematical Sciences, University of Alberta, Edmonton A B, 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.
Mathematics Subject Classification:  35R45, 49J40.

Received: March 2003;      Revised: April 2004;      Available Online: August 2004.