Hölder continuous solutions of an obstacle thermistor problem

Walter Allegretto; Yanping Lin; Shuqing Ma

doi:10.3934/dcdsb.2004.4.983

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2004, Volume 4, Issue 4: 983-997. Doi: 10.3934/dcdsb.2004.4.983

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Hölder continuous solutions of an obstacle thermistor problem

1.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB, Canada T6G 2G1
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: February 28, 2003

Revised: March 31, 2004

Published: October 2004

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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.

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Mathematics Subject Classification: 35R45, 49J40.

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