We consider the Allen–Cahn equation ε2∆u + u − u3 = 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in Rn such that the mean curvature is positive at each boundary point. We show that there exists a sequence εj → 0 such that the Allen–Cahn equation has a solution uεj with an interface which approaches the boundary as j → +∞.

Boundary Interface for the Allen-Cahn Equation

Malchiodi, Andrea;
2007

Abstract

We consider the Allen–Cahn equation ε2∆u + u − u3 = 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in Rn such that the mean curvature is positive at each boundary point. We show that there exists a sequence εj → 0 such that the Allen–Cahn equation has a solution uεj with an interface which approaches the boundary as j → +∞.
2007
Settore MAT/05 - Analisi Matematica
Boundary interfaces; Allen–Cahn equation.
   Variational Methods and Nonlinear Differential Equations
   M.U.R.S.T.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/56118
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