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# A parabolic free boundary problem on flame propagation

### Analysis, Dynamics, and Applications Seminar

A parabolic free boundary problem on flame propagation
Series: Analysis, Dynamics, and Applications Seminar
Location: ONLINE
Presenter: Sunhi Choi, Department of Mathematics, University of Arizona

I will talk about a parabolic free boundary problem, arising from a model for the propagation of equi-diffusional premixed flames with high activation energy. Consider a solution u(x,t) of the heat equation in an unknown domain Ω, which satisfies the following boundary conditions u = 0, |∇u| = 1 on the lateral boundary. If the initial data of u is compactly supported, then the solution vanishes in a finite time T, which is called the extinction time. I will talk about the asymptotic behavior of a solution near its extinction time, and will give a quantitative estimate on the flatness of the free boundary. Then it will turn out that the solution is asymptotically self-similar and the free boundary is a graph of $C^{1+\gamma, \gamma}$ function.

Zoom: https://arizona.zoom.us/j/99410014231