We consider the problem of finding pairs (λ, u), with λ > 0 and u a harmonic function in a three-dimensional torus-like domain D, satisfying the nonlinear boundary condition ∂νu = λ sinh u on ∂D. This type of boundary condition arises in corrosion modeling (Butler-Volmer condition). We prove the existence of solutions which concentrate along some geodesics of the boundary ∂D as the parameter λ goes to zero.
Concentration along geodesics for a nonlinear Steklov problem arising in corrosion modeling
PIEROTTI, DARIO GIANCARLO;
2016-01-01
Abstract
We consider the problem of finding pairs (λ, u), with λ > 0 and u a harmonic function in a three-dimensional torus-like domain D, satisfying the nonlinear boundary condition ∂νu = λ sinh u on ∂D. This type of boundary condition arises in corrosion modeling (Butler-Volmer condition). We prove the existence of solutions which concentrate along some geodesics of the boundary ∂D as the parameter λ goes to zero.File in questo prodotto:
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