Abstract
We study the evolution of unstable front in reaction diffusion systems analytically and derive the evolution equation for the fronts of a bistable system in the presence of advection. As an issue, we investigate the stability of planar fronts and explicitly show that the coupling to advection on the basis of the model of active fluids' or, alternatively, on the model of an interfacial reaction can lead to an instability of the front, eventually leading to a fractalization of the chemical fronts.