Pushed fronts in a Fisher-KPP-Burgers system using geometric desingularization

Matt Holzer, Matthew Kearney, Samuel Molseed, Katie Tuttle, David Wigginton

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves existence of a monotone decreasing, steep (pushed) traveling front for the inviscid FKPP–Burgers system at large ρ and derives the selected speed c̃*(ρ) ∼ (3√3/2) ρ^{1/3} via a conserved-quantity reduction to a planar TW-ODE, a large-ρ scaling (ρ = ε^{-3}), and a quasi-homogeneous blow-up that enables an Implicit Function Theorem argument around the singular limit; this is exactly the structure used in the model’s solution. Minor stylistic differences aside (notation, an explicit leading-order mismatch formula posited by the model), the approaches and conclusions coincide.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript rigorously establishes existence and selection of a pushed front with sharp leading-order speed in a coupled FKPP–Burgers system via a clean combination of singular-limit integration, quasi-homogeneous blow-up, and an implicit-function argument. The methodology is of broad utility for related fast–slow front problems. Minor clarifications—especially around uniqueness, the role of steepness as W\^{ss} landing, and a brief road map of the two blow-up charts—would further improve accessibility.