  We consider the model of auto-ignition (thermal explosion) of a free round
reactive turbulent jet. This model falls into the general class of Gelfand-type
problems and constitutes a boundary value problem for a certain semi-linear
elliptic equation that depends on two parameters: $\alpha$ characterizing the
flow rate and $\lambda$ (Frank-Kamentskii parameter) characterizing the
strength of the reaction. Similarly to the classical Gelfand problem, this
equation admits a solution when the Frank-Kametskii parameter $\lambda$ does
not exceed some critical value $\lambda^*(\alpha)$ and admits no solutions for
larger values of $\lambda$. We obtain the sharp asymptotic behavior of the
critical Frank-Kamenetskii parameter in the strong flow limit ($\alpha\gg1$).
We also provide a detailed description of the extremal solution (i.e., the
solution corresponding to $\lambda^*$) in this regime.
