Regularity and asymptotic behavior of laminar flames in higher dimensions

TL;DR

This paper investigates the behavior of laminar flames in higher dimensions, providing quantitative estimates on free boundary flatness and proving asymptotic sphericity and self-similarity of solutions in a high activation energy model.

Contribution

It introduces new quantitative estimates on free boundary flatness and establishes asymptotic sphericity and self-similarity for solutions in a higher-dimensional flame propagation model.

Findings

Free boundary becomes asymptotically spherical.

Solutions exhibit asymptotic self-similarity.

Quantitative flatness estimates of the free boundary.

Abstract

We study a parabolic free boundary problem, arising from a model for the propagation of equi-diffusional premixed flames with high activation energy. If an initial data is compactly supported, then the solution vanishes in a finite time, called the extinction time. In this paper, we give a quantitative estimate on the flatness of the free boundary and prove that the free boundary is asymptotically spherical and the solution is asymptotically self-similar.