Traveling wave solutions of competitive models withfree boundaries

Jian Yang; Bendong Lou

doi:10.3934/dcdsb.2014.19.817

Article Contents

2014, Volume 19, Issue 3: 817-826. Doi: 10.3934/dcdsb.2014.19.817

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Traveling wave solutions of competitive models with free boundaries

Jian Yang^1, and
Bendong Lou^2,

1.
Department of Mathematics, Tongji University, Shanghai, 200092
2.
Department of Mathematics, Tongji University, Shanghai 200092

Received: June 30, 2013

Revised: August 31, 2013

Published: April 2014

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Abstract

We study two systems of reaction diffusion equations with monostable or bistable type of nonlinearities and with free boundaries. These systems are used as multi-species competitive model. For two-species models, we prove the existence of traveling wave solutions, each of which consists of two semi-waves intersecting at the free boundary. For three-species models, we also obtain some traveling wave solutions. In this case, however, every traveling wave solution consists of two semi-waves and one compactly supported wave in between, each intersecting with its neighbors at the free boundaries.

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Mathematics Subject Classification: Primary: 35K57, 35C07; Secondary: 35R35.

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