Entire solutions of time periodic bistable Lotka–Volterra competition-diffusion systems in $${\mathbb {R}}^N$$

2021 ◽  
Vol 60 (1) ◽  
Author(s):  
Wei-Jie Sheng ◽  
Mingxin Wang ◽  
Zhi-Cheng Wang
Keyword(s):  
Entire Solutions ◽  
Diffusion Systems ◽  
Time Periodic ◽  
Competition Diffusion

Asymptotic spreading of competition diffusion systems: The role of interspecific competitions

2012 ◽  
Vol 23 (6) ◽  
pp. 669-689 ◽  
Author(s):  
GUO LIN ◽  
WAN-TONG LI
Keyword(s):  
Comparison Principle ◽  
Population Densities ◽  
Competitive Systems ◽  
Diffusion Systems ◽  
Negative Role ◽  
Asymptotic Spreading ◽  
Competition Diffusion

This paper is concerned with the asymptotic spreading of competition diffusion systems, with the purpose of formulating the propagation modes of a co-invasion–coexistence process of two competitors. Using the comparison principle for competitive systems, some results on asymptotic spreading are obtained. Our conclusions imply that the interspecific competitions slow the invasion of one species and decrease the population densities in the coexistence domain. Therefore, the interspecific competitions play a negative role in the evolution of competitive communities.

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.

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