Generation of interface for an Allen-Cahn equation with nonlinear diffusion

2009/09/18 by Matthieu Alfaro, Alfaro, Matthieu, Danielle Hilhorst +1
Materials Science · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Solidification and crystal growth phenomena #math.AP

paper · pdf · doi:10.48550/arxiv.0909.3503

arxiv created 2009/09/18 · openalex publication_date 2009/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.

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