Stability of travelling waves for degenerate reaction-diffusion equations of KPP-type

2002 ◽  
Vol 2 (4) ◽  
Author(s):  
Zsolt Biró
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behaviour ◽  
Travelling Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
The Cauchy Problem ◽  
Nonlinear Degenerate

AbstractThe aim of this paper is to investigate the asymptotic behaviour as t → ∞ of the solutions to the Cauchy problem for the nonlinear degenerate KPP-type diffusion-reaction equation u

scholarly journals Interaction of Traveling Curved Fronts in Bistable Reaction-Diffusion Equations in R2

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Nai-Wei Liu
Keyword(s):  
Cauchy Problem ◽  
Initial Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
The Cauchy Problem ◽  
Subsolutions And Supersolutions

We consider the interaction of traveling curved fronts in bistable reaction-diffusion equations in two-dimensional spaces. We first characterize the growth of the traveling curved fronts at infinity; then by constructing appropriate subsolutions and supersolutions, we prove that the solution of the Cauchy problem converges to a pair of diverging traveling curved fronts in R2 under appropriate initial conditions.

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.

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