Mechanism of burning of hydrogen
Martin - マーチン has given excellent answer here. I'll give here an supporting review article for your benefit, which also gives some mathematical overview: 


Louis S. Kassel, “The Mechanism of the Combustion of Hydrogen,” Chem. Rev. 1937, 21(2), 331–345 (DOI: 10.1021/cr60069a010).


Overall, mechanism can be summerized as follows:
\begin{align}
\ce{H2 + \text{heat} &amp;-&gt; 2 H^.}\\
\ce{H^. + O2 &amp;-&gt; HO-O^.}\\
\ce{HO-O^. + H2 &amp;-&gt; HO-OH + H^.}\\
\ce{H^. + HO-OH &amp;-&gt; H2O + HO^.}\\
\ce{HO^. + H2 &amp;-&gt; H2O + H^.}
\end{align}

The propagation would continue with having $\ce{H^.}$ at the end and the presence of excess $\ce{O2}$.