Numerical Solution of Travelling Waves for Reaction-Diffusion Equations Via the Sinc-Galerkin Method

1991 ◽  
pp. 95-113 ◽  
Author(s):  
Jack D. Dockery
Keyword(s):  
Galerkin Method ◽  
Numerical Solution ◽  
Travelling Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

Travelling waves for delayed reaction–diffusion equations with global response

2005 ◽  
Vol 462 (2065) ◽  
pp. 229-261 ◽  
Author(s):  
Teresa Faria ◽  
Wenzhang Huang ◽  
Jianhong Wu
Keyword(s):  
Travelling Waves ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Index Formula ◽  
Delayed Response ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Non Local

We develop a new approach to obtain the existence of travelling wave solutions for reaction–diffusion equations with delayed non-local response. The approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain Banach space, coupled with an index formula of the associated Fredholm operator and some careful estimation of the nonlinear perturbation. The general result relates the existence of travelling wave solutions to the existence of heteroclinic connecting orbits of a corresponding functional differential equation, and this result is illustrated by an application to a model describing the population growth when the species has two age classes and the diffusion of the individual during the maturation process leads to an interesting non-local and delayed response for the matured population.

scholarly journals Bistable travelling waves for nonlocal reaction diffusion equations

2014 ◽  
Vol 34 (5) ◽  
pp. 1775-1791 ◽  
Author(s):  
Matthieu Alfaro ◽  
◽  
Jérôme Coville ◽  
Gaël Raoul ◽  
◽  
...  
Keyword(s):  
Travelling Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Nonlocal Reaction
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