*(English)*Zbl 0714.34042

New results concerning nonadiabatic travelling waves and their singular limits are presented. By means of standard combustion approximations the model reduces to a two-point boundary value problem on the real line with an eigenvalue:

Here u denotes the reduced temperature, v the reactant mass fraction, c the reduced mass flux, f the reduced source term, $\lambda $ the reduced heat loss rate in the hot gases, and g the reduced heat loss rate function.

The natural problem would be to find a nontrivial solution (u,v,c), with (u,v)$\ne (0,1)$ and $c>0$. Existence of a solution is achieved by first considering the problem in a bounded domain and then by taking an infinite domain limit. The author proves strong convergence of the nonadiabatic travelling wave to singular limit free-boundary solutions with discontinuous derivatives.