Diffusive stability against nonlocalized perturbations of planar wave trains in reaction-diffusion systems
type: Item
instance of: scholarly article
title: Diffusive stability against nonlocalized perturbations of planar wave trains in reaction-diffusion systems
zbMATH Open document ID: 1401.35196
author: Björn de Rijk
author: B. Sandstede
published in: Journal of Differential Equations
publication date: 2018-09-04T00:00:00Z
review text: The authors study the stability of planar wave trains in a semi-linear weakly-coupled reaction-diffusion system. It is worth mentioning that planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. As central result, nonlinear diffusive stability is proven against perturbations that are bounded along a line and decay exponentially in the distance from this line.
reviewed by: Adrian Muntean
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 6931742
zbMATH Keywords: nonlinear stability
zbMATH Keywords: pointwise estimates
zbMATH Keywords: nonlocalized perturbations
zbMATH Keywords: planar reaction-diffusion systems
zbMATH Keywords: periodic traveling waves
Wikidata QID: Q60143858
MaRDI profile type: Publication
full work available at URL: j.jde.2018.07.011
OpenAlex ID: W2795007933
cites work: Nonlinear stability of source defects in the complex Ginzburg–Landau equation
cites work: Renormalization group and asymptotics of solutions of nonlinear parabolic equations
cites work: Dichotomies in stability theory
cites work: Spectra and Stability of Spatially Periodic Pulse Patterns II: The Critical Spectral Curve
cites work: The dynamics of modulated wave trains
cites work: Geometric theory of semilinear parabolic equations
cites work: Pointwise Green's function bounds for multidimensional scalar viscous shock fronts
cites work: Mixing in reaction-diffusion systems: large phase offsets
cites work: Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability
cites work: Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation
cites work: Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case
cites work: Nonlinear Stability of Periodic Traveling-Wave Solutions of Viscous Conservation Laws in Dimensions One and Two
cites work: Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction-diffusion equations
cites work: Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves
cites work: Pointwise nonlinear stability of nonlocalized modulated periodic reaction-diffusion waves
cites work: Perturbation theory for linear operators.
cites work: Analytic semigroups and optimal regularity in parabolic problems
cites work: Stability of periodic solutions of conservation laws with viscosity: Pointwise bounds on the Green function
cites work: Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions
cites work: Q4185363
cites work: Q4867883
cites work: On the stability of periodic travelling waves with large spatial period
cites work: Diffusive mixing of periodic wave trains in reaction-diffusion systems
cites work: Diffusive stability of Turing patterns via normal forms
cites work: Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
cites work: Diffusive stability of rolls in the two–dimensional real and complex swift–hohenberg equation
cites work: Pointwise semigroup methods and stability of viscous shock waves
DOI: 10.1016/J.JDE.2018.07.011
description: scientific article; zbMATH DE number 6931742