Wavefront propagation for reaction-diffusion systems of PDE

M. I. Freidlin has introduced probabilistic techniques to study propagation for systems of reaction-diffusion PDE. The motivating idea is that should a reaction-diffusion system possess only a single unstable and a single stable equilibrium, then the solution u of the system will presumably tend to «switch» for large times from near the former to near the latter state. This paper brings to bear purely PDE techniques to this problem, especially the theory of viscosity solutions on Hamilton-Jacobi equations, due to Crandall-Lions