Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order

A family of exact solutions of an evolution equation describing the combustion process in a medium with a power-law temperature dependence of the source density is found. A formal asymptotics of the solution of the initial boundary value problem for the reaction-diffusion equation is constructed. The correctness of the partial sum of an asymptotic series is proved using the method of differential inequalities.