Pattern and velocity selection of fronts propagating in modulated media

We study the problem of pattern and velocity selection of morphologically stable two-dimensional fronts propagating in a spatially modulated medium. The generic system is governed by a local equation and evolves towards a non-trivial steady state with a spatial structure which arises from non-local competition effects and does not necessarily mimic the local structure externally fixed by the modulation. The dynamical process leading to this steady state is studied both analytically and numerically.