Existence of nonplanar solutions of a simple model of premixed Bunsen flames

This work deals with the existence of solutions of a reaction-diffusion equ ation in the plane R-2. The problem, whose unknowns are the real c and the function u, is the following: [GRAPHICS] where 0 < alpha less than or equal to pi/2 is given, (e) over right arrow(2 ) = (-1, 0), and, for any angle phi and any unit vector (e) over right arro w, C ((e) over right arrow, phi) denotes the open half-cone with angle phi around the vector (e) over right arrow. The given function f is of the "ign ition temperature" type. In this paper, we show the existence of a solution (c, u) of (P) and we give an explicit formula that relates the speed c and the angle alpha.