Abstract

In this paper we study, analytically and numerically, the existence and blow up of solutions to two-dimensional boundary value problems of the form Δuλ=0 in Ω, ∂uλ/∂n=Duλ+λf(uλ) on ∂Ω. We place particular emphasis on f(u)=sinh(u)=(eu−e−u)2, in which case the nonlinear flux boundary condition is frequently associated with the names of Butler and Volmer.

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