# American Institute of Mathematical Sciences

March  2013, 8(1): 379-395. doi: 10.3934/nhm.2013.8.379

## Traveling fronts of pyramidal shapes in competition-diffusion systems

 1 Center for Partial Differential Equations, East China Normal University, Minhang, Shanghai, 200241, China 2 Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1-W8-38 Ookayama, Meguro-ku, Tokyo 152-8552

Received  January 2012 Revised  March 2013 Published  April 2013

It is well known that a competition-diffusion system has a one-dimensional traveling front. This paper studies traveling front solutions of pyramidal shapes in a competition-diffusion system in $\mathbb{R}^N$ with $N\geq 2$. By using a multi-scale method, we construct a suitable pair of a supersolution and a subsolution, and find a pyramidal traveling front solution between them.
Citation: Wei-Ming Ni, Masaharu Taniguchi. Traveling fronts of pyramidal shapes in competition-diffusion systems. Networks & Heterogeneous Media, 2013, 8 (1) : 379-395. doi: 10.3934/nhm.2013.8.379
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