Special Session 12: Complexity in reaction-diffusion systems

Contents

This paper studies traveling fronts to cooperative diffusion systems
in $\mathbb{R}^{N}$ for $N\geq 3$. We consider $(N-2)$-dimensional
smooth surfaces as boundaries of strictly convex compact sets in
$\mathbb{R}^{N-1}$. We prove that there exists a traveling front
associated with a given surface and that it is asymptotically stable for
given initial perturbation. The associated traveling fronts coincide up
to phase transition if and only if the given surfaces satisfy an
equivalence relation.