Convex compact sets in RN−1RN−1 give traveling fronts of cooperation–diffusion systems in RNRN

This paper studies traveling fronts to cooperation–diffusion systems in RNRN for N≥3N≥3. We consider (N−2)(N−2)-dimensional smooth surfaces as boundaries of strictly convex compact sets in RN−1RN−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.