Multiplicity and stability of two-dimensional reaction-diffusion equations

2001 ◽  
Author(s):  
Lei Qu
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Two Dimensional

scholarly journals A three‐level time‐split MacCormack method for two‐dimensional nonlinear reaction‐diffusion equations

2020 ◽  
Vol 92 (12) ◽  
pp. 1681-1706 ◽  
Author(s):  
Eric Ngondiep ◽  
Nabil Kerdid ◽  
Mohammed Abdulaziz Mohammed Abaoud ◽  
Ibrahim Abdulaziz Ibrahim Aldayel
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Nonlinear Reaction ◽  
Maccormack Method

Stripes or spots? Nonlinear effects in bifurcation of reaction—diffusion equations on the square

1991 ◽  
Vol 434 (1891) ◽  
pp. 413-417 ◽  
Keyword(s):  
Pattern Formation ◽  
General Pattern ◽  
Reaction Diffusion ◽  
Nonlinear Effects ◽  
Neural Nets ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Linearized Model ◽  
Selection Of

Bifurcation to spatial patterns in a two-dimensional reaction—diffusion medium is considered. The selection of stripes versus spots is shown to depend on the nonlinear terms and cannot be discerned from the linearized model. The absence of quadratic terms leads to stripes but in most common models quadratic terms will lead to spot patterns. Examples that include neural nets and more general pattern formation equations are considered.

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.

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