Solutions for the microsensor thermistor equations in the small bias case
W. Allegretto, Hua Wally Xie · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1993
Synopsis The behaviour of a microsensor thermistor is described by a system of nonlinear coupled elliptic equations subject to mixed Dirichlet-Neumann boundary conditions, to be solved on different domains. We employ the Implicit Function Theorem in Banach space to show that the system has a solution for small applied bias. It does not appear that earlier approaches for similar thermistor problems can be employed in this physically important situation. The fact that the problem is cast in a subset of R 3 is significant in our presentation.