The impact of a wind switch on the stability of traveling fronts in a reaction-diffusion model of fire propagation

The paper’s Proposition 1 states the admissible-speed interval with reversed inequalities (it claims ĉ+α < c < ĉ+β when α>β), which contradicts the phase-plane straddling condition and the constant-w limit; the correct interval is ĉ+β < c < ĉ+α for α>β (and the reverse when α<β). This sign reversal is repeated later when describing the stable range, although figures and endpoints match the corrected interpretation. Apart from this, the paper’s qualitative conclusions—type 1 stable (α>β), type 2 unstable (α<β); a spectrally preferred interior speed with broken translational invariance; and the switch ahead of the fireline—agree with the candidate solution. The model correctly fixes the speed inequalities and gives a coherent Liouville/point-interaction argument for the stability split. Note: the model’s Rayleigh-quotient algebra includes a small inconsistency, but its conclusions are still correct and can be repaired by a standard perturbation argument from the constant-w endpoints.