Analysis, Dynamics and Applications Seminar

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        
Password: “arizona” (all lower case)