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.
2016
corrosion modeling, blowing-up solution, boundary concentration
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/865633
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