Abstract

We consider the singular perturbation problem where , β is a Lipschitz continuous function such that β > 0 in (0, 1), β ≡ 0 outside (0, 1) and . We construct an example exhibiting a degenerate singularity as ε k ↘ 0. More precisely, there is a sequence of solutions u ε k → u as k → ∞, and there exists x 0 ∈ ∂{u > 0} such that Known results suggest that this singularity must be unstable, which makes it hard to capture analytically and numerically. Our result answers a question raised by Jean–Michel Roquejoffre at the FBP'08 in Stockholm.

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