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 nonlinears Steklov problem arising in corrosion modeling / Pagani, Carlo D.; Pierotti, Dario; Pistoia, Angela; Vaira, Giusi. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 48:2(2016), pp. 1085-1108. [10.1137/15M1027024]
Concentration along geodesics for a nonlinears Steklov problem arising in corrosion modeling
PISTOIA, Angela;
2016
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 | Dimensione | Formato | |
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