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QUENCHING OF FLAMES BY FLUID

We consider a simple scalar reaction-advection-diiusion equation with ignition-type nonlinearity and discuss the following question: What kinds of velocity prooles are capable of quenching any given ame, provided the velocity's amplitude is adequately large? Even for shear ows, the answer turns out to be surprisingly subtle. If the velocity proole changes in space so that it is nowhere identically constant, (or if it is identically constant only in a region of small measure) then the ow can quench any initial data. But if the velocity proole is identically constant in a sizable region, then the ensuing ow is incapable of quenching large enough ames, no matter how much larger is the amplitude of this velocity. The constancy region must be wider across than a couple of laminar propagating front-widths. The proof uses a linear PDE associated to the nonlinear problem and quenching follows when the PDE is hypoelliptic. The techniques used allow the derivation of new, nearly optimal bounds on the speed of traveling wave solutions. 1. Introduction We consider a mixture of reactants interacting in a region that may have a rather complicated spatial structure but is thin across. A mathematical model that describes a chemical