scholarly journals Pointwise asymptotic behavior of modulated periodic reaction–diffusion waves

2012 ◽  
Vol 253 (6) ◽  
pp. 1807-1861 ◽  
Author(s):  
Soyeun Jung
Keyword(s):  
Asymptotic Behavior ◽  
Reaction Diffusion ◽  
Diffusion Waves ◽  
Periodic Reaction

scholarly journals Nonlocalized Modulation of Periodic Reaction Diffusion Waves: Nonlinear Stability

2012 ◽  
Vol 207 (2) ◽  
pp. 693-715 ◽  
Author(s):  
Mathew A. Johnson ◽  
Pascal Noble ◽  
L. Miguel Rodrigues ◽  
Kevin Zumbrun
Keyword(s):  
Nonlinear Stability ◽  
Reaction Diffusion ◽  
Diffusion Waves ◽  
Periodic Reaction

scholarly journals Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation

2012 ◽  
Vol 207 (2) ◽  
pp. 669-692 ◽  
Author(s):  
Mathew A. Johnson ◽  
Pascal Noble ◽  
L. Miguel Rodrigues ◽  
Kevin Zumbrun
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Waves ◽  
Periodic Reaction ◽  
Whitham Equation

scholarly journals L1(R)-Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Soyeun Jung
Keyword(s):  
Nonlinear Stability ◽  
Phase Function ◽  
Reaction Diffusion ◽  
Young Inequality ◽  
Spectral Stability ◽  
Stability Conditions ◽  
Pointwise Estimates ◽  
Diffusion Waves ◽  
Periodic Reaction ◽  
Modulational Stability

Assuming spectral stability conditions of periodic reaction-diffusion waves u¯(x), we consider L1(R)-nonlinear stability of modulated periodic reaction-diffusion waves, that is, modulational stability, under localized small initial perturbations with nonlocalized initial modulations. Lp(R)-nonlinear stability of such waves has been studied in Johnson et al. (2013) for p≥2 by using Hausdorff-Young inequality. In this note, by using the pointwise estimates obtained in Jung, (2012) and Jung and Zumbrun (2016), we extend Lp(R)-nonlinear stability (p≥2) in Johnson et al. (2013) to L1(R)-nonlinear stability. More precisely, we obtain L1(R)-estimates of modulated perturbations u~(x-ψ(x,t),t)-u¯(x) of u¯ with a phase function ψ(x,t) under small initial perturbations consisting of localized initial perturbations u~(x-h0(x),0)-u¯(x) and nonlocalized initial modulations h0(x)=ψ(x,0).

Analysis of reaction–diffusion waves in the ferroin-catalysed Belousov–Zhabotinsky reaction

1999 ◽  
Vol 1 (19) ◽  
pp. 4595-4599 ◽  
Author(s):  
Annette F. Taylor ◽  
Vilmos Gáspár ◽  
Barry R. Johnson ◽  
Stephen K. Scott
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Waves ◽  
Belousov Zhabotinsky Reaction

scholarly journals Asymptotic Behavior of Solutions to Reaction-Diffusion Equations with Dynamic Boundary Conditions and Irregular Data

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yonghong Duan ◽  
Chunlei Hu ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as L1-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in L1(Ω¯,dν). This extends the corresponding results in the literatures.

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