Nonplanar traveling fronts in reaction–diffusion equations with combustion and degenerate Fisher-KPP nonlinearities

This paper is concerned with nonplanar traveling fronts in reaction–diffusion equations with combustion nonlinearity and degenerate Fisher-KPP nonlinearity. Our study contains two parts: in the first part we establish the existence of traveling fronts of pyramidal shape in R3R3, and in the second part we establish the existence and stability of V-shaped traveling fronts in R2R2.