Concentration along geodescis for a nonlinear Steklov problem arising in corrosion modelling

We consider the problem of finding pairs $(λ; u)$, with $λ> 0$ and $u$ a harmonic function in a three dimensional torus-like domain, satisfying the nonlinear boundary condition $\partial_ν u = λ\sinh u$ on the boundary. This type of boundary condition arises in corrosion modelling (Butler Volmer condition). We prove existence of solutions which concentrate along some geodesics of the boundary as the parameter $λ$ goes to zero.

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