The diffusive logistic model with a free boundary and seasonalsuccession

Rui Peng; Xiao-Qiang Zhao

doi:10.3934/dcds.2013.33.2007

Article Contents

2013, Volume 33, Issue 5: 2007-2031. Doi: 10.3934/dcds.2013.33.2007

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The diffusive logistic model with a free boundary and seasonal succession

Rui Peng^1, and
Xiao-Qiang Zhao^2,

1.
Department of Mathematics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, China, and Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7

Received: December 2011

Revised: April 2012

Published: May 2013

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Abstract

This paper concerns a diffusive logistic equation with a free boundary and seasonal succession, which is formulated to investigate the spreading of a new or invasive species, where the free boundary represents the expanding front and the time periodicity accounts for the effect of the bad and good seasons. The condition to determine whether the species spatially spreads to infinity or vanishes at a finite space interval is derived, and when the spreading happens, the asymptotic spreading speed of the species is also given. The obtained results reveal the effect of seasonal succession on the dynamical behavior of the spreading of the single species.

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Mathematics Subject Classification: Primary: 35K20, 35R35; Secondary: 35J60, 92B05.

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