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
A nonlinear Steklov problem arising in corrosion modeling
PIEROTTI, DARIO GIANCARLO;VERZINI, GIANMARIA;
2015-01-01
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 numericallyFile in questo prodotto:
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