A nonlinear elliptic boundary value problem related to corrosion modeling

Vogelius, Michael; Xu, Jian-Ming

doi:10.1090/qam/1637048

Authors: Michael Vogelius and Jian-Ming Xu
Journal: Quart. Appl. Math. 56 (1998), 479-505
MSC: Primary 35J65; Secondary 35Q72, 73B99, 73C99
DOI: https://doi.org/10.1090/qam/1637048
MathSciNet review: MR1637048
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Abstract: We study a nonlinear boundary value problem arising from electrochemistry. The essential difficulties are due to the strong nonlinear nature of part of the boundary condition. This part of the boundary condition is of an exponential type and is normally in the corrosion literature associated with the names of Butler and Volmer. We examine the questions of existence and uniqueness of solutions to this boundary value problem. In a numerical example we compare the behaviour of the solutions to the nonlinear problem with the behaviour of the solutions to a corresponding linearized problem. In contrast to earlier studies we put a major emphasis on studying parameter values that may be relevant for the case in which part of the boundary is in a transition to passivity—in practice most likely because it is nearly covered by an oxide layer.

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