Convex compact sets in RN-1 give traveling fronts of cooperation-diffusion systems in RN

This paper studies traveling fronts to cooperation-diffusion systems in RN for N≥3. We consider (N-2)-dimensional smooth surfaces as boundaries of strictly convex compact sets in RN-1, and define an equivalence relation between them. We prove that there exists a traveling front associated with a given surface and show its stability. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation.