scholarly journals Traveling fronts and entire solutions in partially degenerate reaction-diffusion systems with monostable nonlinearity

2013 ◽  
Vol 33 (2) ◽  
pp. 921-946 ◽  
Author(s):  
Shi-Liang Wu ◽  
◽  
Yu-Juan Sun ◽  
San-Yang Liu ◽  
◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Entire Solutions ◽  
Reaction Diffusion Systems ◽  
Traveling Fronts ◽  
Diffusion Systems ◽  
Monostable Nonlinearity

Entire solutions for some reaction–diffusion systems

2015 ◽  
Vol 08 (04) ◽  
pp. 1550052 ◽  
Author(s):  
Guangying Lv ◽  
Dang Luo
Keyword(s):  
Classical Solution ◽  
General Model ◽  
Reaction Diffusion ◽  
Entire Solution ◽  
Reaction Model ◽  
Entire Solutions ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Time Variables ◽  
Belousov Zhabotinskii Reaction

This paper is concerned with the existence of entire solutions of some reaction–diffusion systems. We first consider Belousov–Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables. At last, we give some examples to explain our results for the general models.

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.

Sign in / Sign up

Export Citation Format

Share Document