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January
5, 2001 Abstract |
| Front propagation occurs in many applied problems, such as chemical kinetics, combustion, transport in porous media, and in biology. The basic phenomena can often be described by reaction-diffusion-advection equations. In homogeneous media front propagation has been studied for a long time. However, the study of fronts in inhomogeneous media has begun more recently. Understanding the influence of heterogeneities on the location of fronts, on their profile, and on their speed is of great importance. We study the effects of a periodically varying environment on the speed of fronts. We give a general existence proof of fronts in periodcally varying media close to the homogenization limit. Then we derive a variational principle for their speed. This allows for the calculation of several asymptotic estimates of the velocity. We apply this to the situation of an underlying given fluid flow. In the case of shear flows we show the enhancement of the velocity. Our proofs are based on the maximum principle and therefore further extensions are possible: periodically perforated domains, domains with variable cross section, monotone systems in higher dimensions, discretized diffusion, time dependent coefficients. |