Department of Mathematics, UCI

We consider the problem of quenching the flame in a framework of passive reaction-diffusion model. We ask which flows are more efficient in supressing reaction, and prove bounds on the relationship between flow strength and the initial flame size for different classes of flows. The estimates we prove agree very well with numerical experiments carried out in collaboration with astrophysics ASC group at the University of Chicago. The problem is closely related to proving norm bounds for the evloution semigroup corresponding to the passive scalar model. The techniques involve PDE and probability tools, and further natural questions indicate interesting links with spectral theory of elliptic operators and dynamical systems.