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 Asymptotic behavior of the solutions of a discrete reaction-diffusion equation

2002 ◽  
Vol 29 (5) ◽  
pp. 257-264
Author(s):  
Rigoberto Medina ◽  
Sui Sun Cheng
Keyword(s):  
Asymptotic Behavior ◽  
Diffusion Equation ◽  
Asymptotic Representation ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Asymptotic Representation Of Solutions ◽  
Representation Of Solutions

By means of Bihari type inequalities, we derive sufficient conditions for solutions of a discrete reaction-diffusion equation to be bounded or to converge to zero. Asymptotic representation of solutions are also derived. Our results yield estimates and explicit attractive regions for the solutions.

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