Alexander Kiselev, University of Wisconsin, Madison
Reaction-diffusion in fluid flow

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