Spreading speed and traveling wavefront of an age-structured  populationdiffusing in a 2D lattice strip

Peixuan Weng

doi:10.3934/dcdsb.2009.12.883

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2009, Volume 12, Issue 4: 883-904. Doi: 10.3934/dcdsb.2009.12.883

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Spreading speed and traveling wavefront of an age-structured population diffusing in a 2D lattice strip

Peixuan Weng^1,

1.
School of Mathematics, South China Normal University, Guangzhou 510631

Received: June 30, 2008

Revised: March 31, 2009

Published: October 2009

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Abstract

We derive an age-structured population model for the growth of a single species on a 2-dimensional (2D) lattice strip with Neumann boundary conditions. We show that the dynamics of the mature population is governed by a lattice reaction-diffusion system with delayed global interaction. Using theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows, we obtain the asymptotic speed of spread $c^$*, the nonexistence of traveling wavefronts with wave speed $0 < c < c^$*, and the existence of traveling wavefront connecting the two equilibria $w\equiv 0$ and $w\equiv w^+$ for $c\geq c^$*.

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Mathematics Subject Classification: Primary: 34K31, 34K25; Secondary: 92D25.

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