Perturbation theory for the one-dimensional reaction–diffusion equation with a quadratic nonlinearity of coalescence/annihilation type

2010 ◽  
Vol 81 (5) ◽  
pp. 055802
Author(s):  
E Abad ◽  
H L Frisch
Keyword(s):  
Perturbation Theory ◽  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Quadratic Nonlinearity ◽  
Reaction Diffusion Equation ◽  
One Dimensional ◽  
The One

scholarly journals A reaction-diffusion equation on a thin L-shaped domain

1995 ◽  
Vol 125 (2) ◽  
pp. 283-327 ◽  
Author(s):  
Jack K. Hale ◽  
Geneviève Raugel
Keyword(s):  
Diffusion Equation ◽  
Lower Semicontinuity ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Reaction Diffusion Equation ◽  
Limit Equation ◽  
One Dimensional ◽  
Shaped Domain

We consider a dissipative reaction–diffusion equation on a thin L-shaped domain (with the thinness measured by a parameter ε); we determine the limit equation for ε = 0 and prove the upper semicontinuity of the global attractors at ε = 0. We also state a lower semicontinuity result. When the limit equation is one-dimensional, we prove convergence of any orbit to a singleton.

Nucleation Rate of a Localized Structure in a Reaction-Diffusion System

1993 ◽  
Vol 48 (5-6) ◽  
pp. 636-638 ◽  
Author(s):  
T. Christen
Keyword(s):  
Diffusion Equation ◽  
Nucleation Rate ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reaction Diffusion Equation ◽  
One Dimensional ◽  
Uniform State

Abstract We derive the nucleation rate of a localized structure of a one-dimensional, nonlocal, bistable reaction diffusion equation near instability of the uniform state.

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