Hamilton-Jacobi Equations and Front Motion in Flows

School of Mathematics Colloquium
Thursday, March 14, 2013 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006
Jack Xin – UC Irvine
Greg Blekherman
Front propagation in fluid flows arise in power generation of automobile engines, forest fire spreading, and material interfaces of solidification to name a few. In this talk, we introduce the level set formulation and the resulting Hamilton-Jacobi equation, known as G-equation in turbulent combustion. When the fluid flow has enough intensity, G-equation becomes non-coercive and non-linearity no longer dominates. When front curvature and flow stretching effects are included, the extended G-equation is also non-convex. We discuss recent progress in analysis and computation of homogenization and large time front speeds in cellular flows (two dimensional Hamiltonian flows) from both Lagrangian and Eulerian perspectives, and the recovery of experimental observations from the G-equations.