L 1 ( R ) -Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-11-01
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
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).
American Psychological Association (APA)
Jung, Soyeun. 2017. L 1 ( R ) -Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-7.
https://search.emarefa.net/detail/BIM-1123145
Modern Language Association (MLA)
Jung, Soyeun. L 1 ( R ) -Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves. Advances in Mathematical Physics No. 2017 (2017), pp.1-7.
https://search.emarefa.net/detail/BIM-1123145
American Medical Association (AMA)
Jung, Soyeun. L 1 ( R ) -Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-7.
https://search.emarefa.net/detail/BIM-1123145
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123145