Precise asymptotics for Fisher–KPP fronts

DOI10.1088/1361-6544/aaffe8zbMath1411.35158arXiv1712.02472OpenAlexW2964193117MaRDI QIDQ5742413

Cole Graham

Publication date: 14 May 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.02472

zbMATH Keywords

asymptotic analysisreaction-diffusion equationstravelling front solutionsKPP

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Traveling wave solutions (35C07) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91)

Related Items (14)

The distance between the two BBM leaders ⋮ Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations ⋮ Ahead of the Fisher–KPP front ⋮ Universal selection of pulled fronts ⋮ Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts ⋮ Voting models and semilinear parabolic equations ⋮ Front selection in reaction-diffusion systems via diffusive normal forms ⋮ Reaction-diffusion equations in the half-space ⋮ Cross-overs of Bramson's shift at the transition between pulled and pushed fronts ⋮ The Bramson delay in a Fisher-KPP equation with log-singular nonlinearity ⋮ Global existence for a free boundary problem of Fisher–KPP type ⋮ 1-stable fluctuations in branching Brownian motion at critical temperature. I: The derivative martingale ⋮ Fisher-KPP equation with small data and the extremal process of branching Brownian motion ⋮ Sharp large time behaviour in \(N\)-dimensional reaction-diffusion equations of bistable type

Cites Work

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• Population stabilization in branching Brownian motion with absorption and drift
• On the nonlinear diffusion equation of Kolmogorov, Petrovskij, and Piscunov
• A short proof of the logarithmic Bramson correction in Fisher-KPP equations
• Convergence to a single wave in the Fisher-KPP equation
• Convergence of solutions of the Kolmogorov equation to travelling waves
• Interesting Series Involving the Central Binomial Coefficient
• Maximal displacement of branching brownian motion
• Exact solution and precise asymptotics of a Fisher–KPP type front
• Refined long-time asymptotics for Fisher–KPP fronts
• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts

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