A note on the existence of periodic travelling wave solutions with large periods in generalized reaction-diffusion systems

1983 ◽  
Vol 34 (2) ◽  
pp. 236-240 ◽  
Author(s):  
K. R. Schneider
Keyword(s):  
Reaction Diffusion ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Reaction Diffusion Systems ◽  
Wave Solutions ◽  
Diffusion Systems ◽  
Periodic Travelling Wave

scholarly journals TRAVELLING WAVE SOLUTIONS IN NONLOCAL REACTION–DIFFUSION SYSTEMS WITH DELAYS AND APPLICATIONS

2009 ◽  
Vol 51 (1) ◽  
pp. 49-66 ◽  
Author(s):  
ZHI-XIAN YU ◽  
RONG YUAN
Keyword(s):  
Reaction Diffusion ◽  
Travelling Wave ◽  
Accurate Information ◽  
Travelling Wave Solutions ◽  
Reaction Diffusion Systems ◽  
Competition Models ◽  
Wave Solutions ◽  
Diffusion Systems ◽  
Nonlocal Reaction ◽  
Iteration Technique

AbstractThis paper deals with two-species convolution diffusion-competition models of Lotka–Volterra type with delays which describe more accurate information than the Laplacian diffusion-competition models. We first investigate the existence of travelling wave solutions of a class of nonlocal convolution diffusion systems with weak quasimonotonicity or weak exponential quasimonotonicity by a cross-iteration technique and Schauder’s fixed point theorem. When the results are applied to the convolution diffusion-competition models with delays, we establish the existence of travelling wave solutions as well as asymptotic behaviour.

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