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Traveling wave solutions for a competitive reaction–diffusion system and their asymptotics

✍ Scribed by Xiaojie Hou; Anthony W. Leung

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
935 KB
Volume
9
Category
Article
ISSN
1468-1218

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✦ Synopsis

For a competitive PDE system, we study the existence, uniqueness, and asymptotic behaviors of the traveling wave solutions connecting a monoculture equilibrium to a co-existence equilibrium. We use the method of upper-lower solutions to prove the existence of traveling wave solutions, and investigate the asymptotic behavior of the traveling waves in relation to various interacting parameters of the system. By comparing with the upper solution, we obtain asymptotic description of the solution for large x or t in relation to the interacting parameters, and show the uniqueness of traveling wave solutions connecting the two equilibria with such asymptotic rates. Numerical results are also presented to illustrate the theoretical results.

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Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka–Volterra competition system with diffusion
✍ Guangyu Zhao; Shigui Ruan 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 469 KB

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c(\*) such that for each wave speed c ≤ c(\*), there is a time p