A nonlinear Steklov problem arising in corrosion modeling

Abstract

We investigate the existence of pairs (λ, u), with λ> 0 and u harmonic function in the unit ball B⊂ ℝ3, such that the nonlinear boundary condition ∂νu=λsinhu holds on ∂ B. This type of exponential boundary condition arises in corrosion modeling (Butler-Volmer condition). We prove existence of global branches of nontrivial solutions in the framework of analytic bifurcation theory and investigate their properties both analytically and numerically.