Periodic traveling fronts for partially degenerate reaction-diffusion systems with bistable and time-periodic nonlinearity

Abstract

This paper is concerned with the periodic traveling fronts for partially degenerate reaction-diffusion systems with bistable and time-periodic nonlinearity. We first determine the signs of wave speeds for two monostable periodic traveling fronts of the system. Then, we prove the existence of periodic traveling fronts connecting two stable periodic solutions. An estimate of the wave speed is also obtained. Further, we prove the monotonicity, uniqueness (up to a translation), Liapunov stability and exponentially asymptotical stability of the smooth bistable periodic traveling fronts.

Keywords

• time-periodic reaction-diffusion systems
• periodic traveling fronts
• bistable nonlinearity
• partially degenerate systems
• 35k57
• 37l60
• 92d25