Homogenization of a Nonlinear Elliptic Boundary Value Problem Modelling Galvanic Interactions on a Heterogeneous Surface
Younus Bhat · Kluwer Academic Publishers eBooks · 2006
SummaryWe study a nonlinear elliptic boundary value problem arising from electrochemistry. The boundary value problems occurs in the study of heterogeneous electrode surfaces. The boundary condition is of an exponential type and is normally associated with the names of Butler and Volmer and the notions of galvanic corrosion. We examine the questions of existence and uniqueness of solutions to this boundary value problem. We then treat the problem from the point of view of homogenization theory. The boundary condition has a periodic structure. We find a limiting or effective problem as the period approaches zero, along with a correction term and convergence estimates. We also do numerical experiments to investigate the behaviour of galvanic currents near the boundary as the period approaches zero.