Traveling fronts of pyramidal shapes in competition-diffusion systems

Wei-Ming Ni; Masaharu Taniguchi; Wei-Ming Ni; Masaharu Taniguchi

doi:10.3934/nhm.2013.8.379

Networks and Heterogeneous Media

2013, Volume 8, Issue 1: 379-395. doi: 10.3934/nhm.2013.8.379

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Traveling fronts of pyramidal shapes in competition-diffusion systems

Wei-Ming Ni ^{1
,},
Masaharu Taniguchi ^{2
,}

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

Received: 01 January 2012 Revised: 01 March 2013
Primary: 35C07; Secondary: 35K57.

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.
- Traveling front,
- pyramidal shapes,
- competition-diffusion system
Citation: Wei-Ming Ni, Masaharu Taniguchi. Traveling fronts of pyramidal shapes in competition-diffusion systems[J]. Networks and Heterogeneous Media, 2013, 8(1): 379-395. doi: 10.3934/nhm.2013.8.379

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Abstract

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.

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