Exponentially Small Pinning Effects in Reaction-diffusion Equations

We consider reaction-diffusion systems on infinite cylinders and look for standing or pinned waves. While in the spatial homogeneous situation pinned waves may only exist for exceptional parameter values, one would expect, that waves are pinned at periodic heterogenities for large parameter regions. Using a spatial dynamics approach and an exponential homogenization techniques, we show that these parameter regions are in fact exponentially small in the period of the heterogenities.