Bistable transition fronts in R^N

2013/02/20 by François Hamel, Hamel, Francois
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1302.4817

openalex publication_date 2013/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is chiefly concerned with qualitative properties of some reaction-diffusion fronts. The recently defined notions of transition fronts generalize the standard notions of traveling fronts. In this paper, we show the existence and the uniqueness of the global mean speed of bistable transition fronts in R^N. This speed is proved to be independent of the shape of the level sets of the fronts. The planar fronts are also characterized in the more general class of almost-planar fronts with any number of transition layers. These qualitative properties show the robustness of the notions of transition fronts. But we also prove the existence of new types of transition fronts in R^N that are not standard traveling fronts, thus showing that the notions of transition fronts are broad enough to include other relevant propagating solutions.

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