Transition layer for the heterogeneous Allen–Cahn equation
نویسندگان
چکیده
منابع مشابه
Transition Layer for the Heterogeneous Allen-Cahn Equation
We consider the equation (1) ε∆u = (u− a(x))(u − 1) in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in R, ν the outer unit normal to ∂Ω, and a a smooth function satisfying −1 < a(x) < 1 in Ω. We set K, Ω+ and Ω− to be respectively the zero-level set of a, {a > 0} and {a < 0}. Assuming ∇a 6= 0 on K and a 6= 0 on ∂Ω, we show that there exists a sequence εj → 0 such that equation (1)...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2008
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2007.03.008