Singularly perturbed problem for non-local reaction-diffusion equations involving two small parameters

2006 ◽  
Vol 10 (6) ◽  
pp. 479-483
Author(s):  
Rong-jun Cheng
Keyword(s):  
Local Reaction ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Singularly Perturbed Problem ◽  
Small Parameters ◽  
Non Local

scholarly journals Propagation direction of the bistable travelling wavefront for delayed non-local reaction diffusion equations

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180898
Author(s):  
Manjun Ma ◽  
Jiajun Yue ◽  
Chunhua Ou
Keyword(s):  
Population Biology ◽  
Wave Speed ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Kernel Functions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Non Local ◽  
Selection Mechanisms

For delayed non-local reaction–diffusion equations arising from population biology, selection mechanisms of the speed sign for the bistable travelling wavefront have not been found. In this paper, based on the theory of asymptotic speeds of spread for monotone semiflows, we firstly provide an interval of values of wave speed and a novel general condition for determining the speed sign by applying the comparison principle and the globally asymptotic stability of the bistable travelling wave. Moreover, through constructing novel upper/lower solutions, we give explicit conditions for the speed sign to be positive or negative. The obtained results are efficiently applied to three classical forms of the kernel functions.

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