Temperature distributions for a semilinear reaction — diffusion equation

An important special type of reaction — diffusion equation arising in the classical combustion theory is studied. We systematically obtain admissible classes of solutions having a special type of separation of variables. Of particular interest is a parameter δ ≥ 0. We obtain the critical value of δ, δcr for a solution in a found class. Thus, the problem of self - ignition for a reactor vessel is solved completely. Remarks on some relevant applications of our results are also supplied.