, Volume 182, Issue 2, pp 181-221

Singular Limits of a Two-Dimensional Boundary Value Problem Arising in Corrosion Modelling

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Abstract

We consider the boundary value problem

where Ω is a smooth and bounded domain in ℝ2 and λ > 0. We prove that for any integer k ≧ 1 there exist at least two solutions u λ with the property that the boundary flux satisfies up to subsequences λ → 0,

where the ξ j are points of ∂Ω ordered clockwise in j.

Communicated by P. Rabinowitz