scholarly journals Stability of planar traveling fronts in bistable reaction–diffusion systems

2017 ◽  
Vol 156 ◽  
pp. 42-60
Author(s):  
Wei-Jie Sheng
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Traveling Fronts ◽  
Diffusion Systems

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

2019 ◽  
Vol 9 (1) ◽  
pp. 923-957
Author(s):  
Shi-Liang Wu ◽  
Cheng-Hsiung Hsu
Keyword(s):  
Periodic Solutions ◽  
Wave Speed ◽  
Reaction Diffusion ◽  
Wave Speeds ◽  
Reaction Diffusion Systems ◽  
Liapunov Stability ◽  
Traveling Fronts ◽  
Diffusion Systems ◽  
Stable Periodic ◽  
Time Periodic

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.

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