2011/07/18 by Matthieu Alfaro, Dorothea Hilhorst, Alfaro, Matthieu +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Stochastic processes and statistical mechanics #math.AP
paper · pdf · doi:10.48550/arxiv.1107.3543
arxiv created 2011/07/18 · openalex publication_date 2011/07/18 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We prove the rapid formation of transition layers which then propagate. We prove the convergence to a sharp interface limit whose normal velocity, at each point, is that of the underlying degenerate travelling wave.