We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection-reaction-diffusion systems. 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 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 with speed c>c*.
- Advection-reaction-diffusion system
- Asymptotic stability
- Lotka-Volterra competition system
- Maximal wave speed
- Time periodic traveling waves
ASJC Scopus subject areas
- Applied Mathematics