scholarly journals Nonstandard perturbation approximation and travelling wave solutions of nonlinear reaction diffusion equations

2007 ◽  
Vol 24 (1) ◽  
pp. 217-238 ◽  
Author(s):  
Aditya Kaushik
Keyword(s):  
Reaction Diffusion ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Reaction ◽  
Perturbation Approximation

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.

Travelling wave solutions for reaction-diffusion equations

1997 ◽  
Vol 30 (6) ◽  
pp. 3417-3426
Author(s):  
Zheng-Yuan Li ◽  
Ming-Xin Wang ◽  
Ya-Ping Wu ◽  
Qi-Xiao Ye
Keyword(s):  
Reaction Diffusion ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Travelling Wave Solutions ◽  
Wave Solutions

Stability of fronts and transient behaviour in KPP systems

2010 ◽  
Vol 466 (2118) ◽  
pp. 1769-1788 ◽  
Author(s):  
Anna Ghazaryan ◽  
Peter Gordon ◽  
Alexander Virodov
Keyword(s):  
Reaction Diffusion ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Travelling Wave Solutions ◽  
Transient Behaviour ◽  
Stable Pattern ◽  
Wave Solutions ◽  
Travelling Fronts ◽  
Pressure Driven

We consider a system of two reaction diffusion equations with the Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearity which describes propagation of pressure-driven flames. It is known that the system admits a family of travelling wave solutions parameterized by their velocity. In this paper, we show that these travelling fronts are stable under the assumption that perturbations belong to an appropriate weighted L 2 space. We also discuss an interesting meta-stable pattern the system exhibits in certain cases.

scholarly journals TRAVELLING WAVE SOLUTIONS FOR DOUBLY DEGENERATE REACTION–DIFFUSION EQUATIONS

2010 ◽  
Vol 52 (1) ◽  
pp. 101-109 ◽  
Author(s):  
M. B. A. MANSOUR
Keyword(s):  
Reaction Diffusion ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Travelling Wave Solutions ◽  
Wave Analysis ◽  
Qualitative Behaviour ◽  
Wave Solutions ◽  
Special Case

AbstractThis paper concerns a nonlinear doubly degenerate reaction–diffusion equation which appears in a bacterial growth model and is also of considerable mathematical interest. A travelling wave analysis for the equation is carried out. In particular, the qualitative behaviour of both sharp and smooth travelling wave solutions is analysed. This travelling wave behaviour is also verified by some numerical computations for a special case.

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