Nonlinear hydrodynamic corrections to supersonic F-KPP wave fronts

We study the hydrodynamic corrections to the dynamics and structure of an exothermic chemical wave front of Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) type which travels in a one-dimensional gaseous medium. We show in particular that its long time dynamics, cut-off sensitivity and leading edge behavior are almost entirely controlled by the hydrodynamic front speed correction δU_h which characterizes the pushed nature of the front. Reducing the problem to an effective comoving heterogeneous F-KPP equation, we determine two analytical expressions for δU_h: an accurate one, derived from a variational method, and an approximate one, from which one can assess the δU_h sensitivity to the shear viscosity and heat conductivity of the fluid of interest.