Abstract
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 periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c<c* are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves for nonzero speed c>c*.
Original language | English (US) |
---|---|
Pages (from-to) | 627-671 |
Number of pages | 45 |
Journal | Journal des Mathematiques Pures et Appliquees |
Volume | 95 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2011 |
Keywords
- Asymptotic stability
- Lotka-Volterra competition system
- Maximal wave speed
- Time periodic traveling wave
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics