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Title Convex compact sets in $\mathbb{R}^{N-1}$ give traveling fronts in $\mathbb{R}^{N}$ in cooperative diffusion systems

Name Masaharu Taniguchi
Country Japan
Email taniguchi-m@okayama-u.ac.jp
Submit Time 2014-02-24 21:53:21
Special Session 12: Complexity in reaction-diffusion systems
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.