Monostable waves and spreading speed  for a reaction-diffusion model with seasonal succession

Manjun  Ma; Xiao-Qiang Zhao

doi:10.3934/dcdsb.2016.21.591

Article Contents

2016, Volume 21, Issue 2: 591-606. Doi: 10.3934/dcdsb.2016.21.591

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Monostable waves and spreading speed for a reaction-diffusion model with seasonal succession

Manjun Ma^1, and
Xiao-Qiang Zhao^2,

1.
Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7

Received: July 31, 2014

Revised: October 31, 2014

Published: February 2016

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Abstract

This paper is devoted to the study of propagation phenomena for a two-species competitive reaction-diffusion model with seasonal succession in the monostable case. By appealing to theory of traveling waves and spreading speeds for monotone semiflows, we establish the existence of the minimal wave speed for rightward traveling waves and its coincidence with the rightward spreading speed. We also obtain a set of sufficient conditions for the spreading speed to be linearly determinate.

Keywords:

Mathematics Subject Classification: Primary: 35C07, 35K57; Secondary: 37N25, 92D25.

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