Pattern propagation in nonlinear dissipative systems
type: Item
instance of: scholarly article
title: Pattern propagation in nonlinear dissipative systems
zbMATH Open document ID: 0622.76051
DOI: 10.1016/0167-2789(85)90094-6
author: B. George
published in: Physica D
publication date: 1985-01-01T00:00:00Z
review text: The paper, motivated in a large part by a similarity of pattern propagation in a wide class of continuous systems described by nonlinear parabolic equations, is devoted to a generalization of marginal-stability hypothesis that has been suggested in the theory of dendritic crystal growth. Starting with a nonlinear diffusion problem and ''amplitude'' equation the authors examine different kinds of propagating solutions. They arrive at a conjecture on the validity of marginal-stability principle also away from the threshold for the pattern-forming models. Finally, three different pattern-forming models (the Hohenberg-Swift- Pomeau-Manneville equation, the reaction diffusion equations and the fourth order nonlinear parabolic equation derived in the theory of crystal growth) are solved numerically to support the hypothesis.
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76R99
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 4010064
zbMATH Keywords: pattern propagation
zbMATH Keywords: continuous systems
zbMATH Keywords: nonlinear parabolic equations
zbMATH Keywords: marginal-stability hypothesis
zbMATH Keywords: dendritic crystal growth
zbMATH Keywords: nonlinear diffusion problem
zbMATH Keywords: pattern-forming models
zbMATH Keywords: Hohenberg-Swift-Pomeau- Manneville equation
zbMATH Keywords: reaction diffusion equations
zbMATH Keywords: fourth order nonlinear parabolic equation
reviewed by: Andrzej Tylikowski
MaRDI profile type: Publication
full work available at URL: 0167-2789(85)90094-6
OpenAlex ID: W1983435166
cites work: Q3910190
cites work: Nonlinear dynamics and turbulence
cites work: Hydrodynamic instabilities and the transition to turbulence
cites work: Q4189096
cites work: Phase-winding solutions in a finite container above the convective threshold
cites work: Q4158861
cites work: Multidimensional nonlinear diffusion arising in population genetics
cites work: The Instability of Nonmonotonic Wave Solutions of Parabolic Equations
cites work: On two types of moving front in quasilinear diffusion
description: scientific article; zbMATH DE number 4010064