Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation

Matthieu Alfaro (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We investigate the behavior, as a small parameter tends to zero, of a nonlocal Allen-Cahn equation. Given a rather general initial data, we perform a rigorous analysis of both the generation and the motion of interface, and obtain a new estimate for its thickness. The limit problem involves motion by mean curvature together with a nonlocal effect (which allows the possibility of nontrivial stationary state).

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Alfaro. Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation. Nonlinear Analysis: Theory, Methods and Applications, 2010, pp.72 (2010), no. 7-8, 3324--3336. ⟨10.1016/j.na.2009.12.013⟩. ⟨hal-00392032⟩