A NONLINEAR ELLIPTIC BOUNDARY-VALUE PROBLEM RELATED TO CORROSION MODELING

We study a nonlinear boundary value problem arising from electrochemis try. The essential difficulties are due to the strong nonlinear nature of part of the boundary condition. This part of the boundary conditio n is of an exponential type and is normally in the corrosion literatur e associated with the names of Butler and Volmer. We examine the quest ions of existence and uniqueness of solutions to this boundary value p roblem. In a numerical example we compare the behaviour of the solutio ns to the nonlinear problem with the behaviour of the solutions to a c orresponding linearised problem. In contrast to earlier studies we put a major emphasis on studying parameter values that may be relevant fo r the case in which part of the boundary is in a transition to passivi ty-in practice most likely because it is nearly covered by an oxide la yer.