Traveling waves and spreading speeds for time-space periodic monotone systems

Jian Fang; Xiao Yu; Xiao-Qiang Zhao

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arXiv · 1504.03788

Traveling waves and spreading speeds for time-space periodic monotone systems

Jian Fang·Xiao Yu·Xiao-Qiang Zhao

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Abstract

The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence of time-space periodic traveling waves and spreading speeds. We then apply these abstract results to a two species competition reaction-advection-diffusion model. It turns out that the minimal wave speed exists and coincides with the single spreading speed for such a system no matter whether the spreading speed is linearly determinate. We also obtain a set of sufficient conditions for the spreading speed to be linearly determinate.

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Jian Fang, Xiao Yu, Xiao-Qiang Zhao. 2015-04-15. Traveling waves and spreading speeds for time-space periodic monotone systems. https://arxiv.org/abs/1504.03788

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