9:00 am Saturday, April 17, 2010
Nonlinear Analysis and PDEs Workshop: Homogenization and enhancement for the G-equation in periodic media by Panagiotis Souganidis (University of Chicago) in RLM 6.104
I will present homogenization results about the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, it is shown that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic Lfirst-order (spatio-temporal homogeneous) level set equation. Moreover there is a rate of convergence and, under certain conditions, the averaging enhances the velocity of the underlying front. At scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulf shape associated with the effective Hamiltonian. This is joint work with J. Nolen and P. Cardaliaguet. Submitted by
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