Convergence to a single wave in the Fisher-KPP equation

By James Nolen, Jean-Michel Roquejoffre, Lenya Ryzhik. 2016

52 citations recorded by the source corpus.

The authors study the large time asymptotics of a solution of the Fisher-KPP reaction-diffusion equation, with an initial condition that is a compact perturbation of a step function. A well-known result of Bramson states that, in the reference frame moving as 2t−(3/2)log t+x∞, the solution of the equation converges as t → +∞ to a translate of the traveling wave corresponding to the minimal speed c* = 2. The constant x∞ depends on the initial condition u(0, x). The proof is elaborate, and based on probabilistic arguments. The purpose of this paper is to provide a simple proof based on PDE arguments.

Subfields: Condensed Matter Physics, Mathematical Physics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/405f287dfbce4a814375b4c01b3f7d97112ef5a9

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In Condensed Matter Physics

1. Juan Luis V'azquez
2. A. Audrito

In Mathematical Physics

1. A. Audrito
2. Juan Luis V'azquez
3. Matteo Bonforte
4. G. Grillo

In Public Health, Environmental and Occupational Health

1. Juan Luis V'azquez
2. A. Audrito

Citations in the corpus

• The Fisher–KPP problem with doubly nonlinear “fast” diffusion (2016, result): “More recently, similar results have been proved in [34, 46, 47] with PDEs techniques.”