Stopping a reaction-diffusion front

Reaction-diffusion Front Speed Enhancement by Flows

Abstract. We study flow-induced enhancement of the speed of pulsating traveling fronts for reaction-diffusion equations, and quenching of reaction by fluid flows. We prove, for periodic flows in two dimensions and any combustion-type reaction, that the front speed is proportional to the square root of the (homogenized) effective diffusivity of the flow. We show that this result does not hold in...

Front tracking for quantifying advection-reaction-diffusion.

We present an algorithm for measuring the speed and thickness of reaction fronts, and from those quantities, the diffusivity and the reaction rate of the active chemical species. This front-tracking algorithm provides local measurements suitable for statistics and requires only a sequence of concentration fields. Though our eventual goal is front tracking in advection-reaction-diffusion, here w...

Large scale reaction front dynamics in anisotropic reaction-diffusion systems

A Reaction-Diffusion System with Periodic Front Dynamics

A reaction-diffusion model motivated by Proteus mirabilis swarm colony development is presented and analyzed in this work. The principal variables are the concentrations of swarm cells and swimmer cells, which are multicellular and single-cell forms, respectively, of the Proteus mirabilis bacteria. The kinetic terms model the growth and division process of the swimmer cells, as well as the form...

Stable Foliations near a Traveling Front for Reaction Diffusion Systems

We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel combustion. In this way we complement the orbital stability results from earlier papers by A. Ghazaryan, S. Schecter and Y. Latushkin. The essential spectrum of the di...