Stability of travelling waves for a cross-diffusion model
type: Item
instance of: scholarly article
title: Stability of travelling waves for a cross-diffusion model
zbMATH Open document ID: 0887.35019
author: Yaping Wu
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-05-05T00:00:00Z
review text: The following coupled system of parabolic and ordinary differential equations is investigated: \[ u_t=\rho v-(v-1)^2u-s u+v_{xx}, \qquad v_t=u-hv, \] \((h, \rho, s= \text{const}>0)\). This system is a cross-diffusion model of a mono-species forest with two age classes. By using the theory of strongly continuous nonanalytic semigroups and a detailed spectral analysis, the asymptotic stability of travelling waves is established.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1115422
zbMATH Keywords: system of parabolic and ordinary differential equations
zbMATH Keywords: strongly continuous nonanalytic semigroups
zbMATH Keywords: spectral analysis
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5636
OpenAlex ID: W2083793901
cites work: A cross-diffusion model of forest boundary dynamics
cites work: Geometric theory of semilinear parabolic equations
cites work: Construction of the Leray-Schauder degree for elliptic operators in unbounded domains
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Exponential stability of the semigroup associated with a thermoelastic system
cites work: Q3722900
DOI: 10.1006/JMAA.1997.5636
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description: scientific article; zbMATH DE number 1115422