Development of traveling waves in an interacting two-species chemotaxis model

Tai-Chia Lin; Zhi-An Wang

doi:10.3934/dcds.2014.34.2907

Article Contents

2014, Volume 34, Issue 7: 2907-2927. Doi: 10.3934/dcds.2014.34.2907

This issue Previous Article Generalized exact boundary synchronization for a coupled system of wave equations Next Article Discrete admissibility and exponential trichotomy of dynamical systems

Development of traveling waves in an interacting two-species chemotaxis model

Tai-Chia Lin^1, and
Zhi-An Wang^2,

1.
Institute of Applied Mathematical Sciences, NCTS Taipei Office, National Taiwan University, Taipei 106
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: May 31, 2013

Revised: August 31, 2013

Published: June 2014

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Abstract

By constructing sub and super solutions, we establish the existence of traveling wave solutions to a two-species chemotaxis model, which describes two interacting species chemotactically reacting to a chemical signal that is degraded by the two species. We identify the full parameter regime in which the traveling wave solutions exist, derive the asymptotical decay rates of traveling wave solutions at far field and show that the traveling wave solutions are convergent as the chemical diffusion coefficient goes to zero.

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Mathematics Subject Classification: Primary: 35C07, 35K55, 46N60; Secondary: 62P10, 92C17.

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