A note on interface formation in singularly perturbed elliptic problems

Abstract

In this note, we prove that the equal-area condition is necessary for the formation of internal transition layer by the solutions of a general singularly perturbed elliptic problem. Our result is independent of boundary conditions, it improves previous references in the literature and can be applied to Allen-Cahn, Sine-Gordon and Fisher-KPP equations, for example.

Keywords:

• Internal transition layer
• interface formation
• equal-area condition
• elliptic problem

AMS SUBJECT CLASSIFICATIONS:

• 35B40
• 35B25
• 35J15
• 35J61

Disclosure statement

No potential conflict of interest was reported by the author(s).