Existence and Stability of Traveling Waves for Degenerate Reaction–Diffusion Equation with Time Delay

2018 ◽  
Vol 28 (3) ◽  
pp. 1011-1042 ◽  
Author(s):  
Rui Huang ◽  
Chunhua Jin ◽  
Ming Mei ◽  
Jingxue Yin
Keyword(s):  
Time Delay ◽  
Diffusion Equation ◽  
Traveling Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Existence And Stability

scholarly journals On Asymptotic Behavior for Reaction Diffusion Equation with Small Time Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Xunwu Yin
Keyword(s):  
Asymptotic Behavior ◽  
Time Delay ◽  
Diffusion Equation ◽  
Bounded Solution ◽  
Reaction Diffusion ◽  
Small Time ◽  
Reaction Diffusion Equation ◽  
Small Time Delay ◽  
Scalar Diffusion

We investigate the asymptotic behavior of scalar diffusion equation with small time delayut-Δu=f(ut,u(t-τ)). Roughly speaking, any bounded solution will enter and stay in the neighborhood of one equilibrium when the equilibria are discrete.

scholarly journals Traveling waves for a boundary reaction–diffusion equation

2012 ◽  
Vol 230 (2) ◽  
pp. 433-457 ◽  
Author(s):  
L. Caffarelli ◽  
A. Mellet ◽  
Y. Sire
Keyword(s):  
Diffusion Equation ◽  
Traveling Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Boundary Reaction
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