In combustion, Michelson–Sivashinsky equation describes the evolution of a premixed flame front, subjected to the Darrieus–Landau instability, in the small heat release approximation. The equation was derived by Gregory Sivashinsky in 1977, who along the Daniel M. Michelson, presented the numerical solutions of the equation in the same year. The equation for  (where ), which describes the perturbation amplitude of the planar flame front, reads as
where  is a constant. Incorporating also the Rayleigh–Taylor instability of the flame, the equation modifies to 
where  is the spatially-averaged quantity of , which is a time-dependent function and  is another constant.