| Abstract: |
| This paper is concerned with combustion transition fronts in $\mathbb{R}^{N}$ $(N\geq1)$. Firstly, we prove the existence and the uniqueness of the global mean speed which is independent of the shape of the level sets of the fronts. Secondly, we show that the planar fronts can be characterized in the more general class of almost-planar fronts. Thirdly, we show the existence of new types of transitions fronts in $\mathbb{R}^{N}$ which are not standard traveling fronts. Finally, we prove that all transition fronts are monotone increasing in time, whatever shape their level sets may have. |
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