Traveling wave solutions of a competitive recursion

Guo Lin; Wan-Tong Li

doi:10.3934/dcdsb.2012.17.173

Article Contents

2012, Volume 17, Issue 1: 173-189. Doi: 10.3934/dcdsb.2012.17.173

This issue Previous Article Stability of an efficient Navier-Stokes solver with Navier boundary condition Next Article Stability transitions and dynamics of mesa patterns near the shadow limit of reaction-diffusion systems in one space dimension

Traveling wave solutions of a competitive recursion

Guo Lin^1, and
Wan-Tong Li^2,

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000
2.
School of Mathematic and Statistics, Lanzhou University, Lanzhou, Gansu 730000

Received: March 31, 2010

Revised: February 28, 2011

Published: December 2011

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Abstract

This paper is concerned with the traveling wave solutions of a competitive recursion. By using a cross iteration scheme, we first establish the existence of traveling wave solutions, which are the invasion waves of two competitive invaders. These wave solutions are useful in understanding the long time behavior of solution of the corresponding Cauchy type problem where the initial distribution is a perturbation of the wave profile of a traveling wave solution that may be nonmonotone.

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Mathematics Subject Classification: Primary: 37L15, 39A11; Secondary: 92D25.

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