Near the extinction of the diffusion flame,  is order unity. The equation has no solution for , where  is the extinction Damköhler number. For  with , the equation possess two solutions, of which one is an unstable solution. Unique solution exist if  and . The solution is unique for , where  is the ignition Damköhler number.
Liñán also gave a correlation formula for the extinction Damköhler number, which is increasingly accurate for ,