Nonlinear stability of strong traveling waves for the singular Keller-Segel system with large perturbations
type: Item
instance of: scholarly article
title: Nonlinear stability of strong traveling waves for the singular Keller-Segel system with large perturbations
zbMATH Open document ID: 1397.35318
author: Hongyun Peng
author: Zhi-An Wang
published in: Journal of Differential Equations
publication date: 2018-05-28T00:00:00Z
review text: The authors study the nonlinear stability of traveling wave solutions for a system of parabolic equations in one space dimension \(u_t-\chi(uv)_x=Du_{xx}\), \(v_t+(\varepsilon v^2-u)_x=\varepsilon v_{xx}\), derived from a singular chemotaxis model describing the initiation of tumor angiogenesis. This paper provides a novel result on the asymptotic stability of large amplitude traveling waves with large initial perturbation for a system of conservation laws, although similar results have been available for some scalar equations. Extension of results to the initial data with lower regularity is also given.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 6875586
zbMATH Keywords: chemotaxis
zbMATH Keywords: traveling wave solutions
zbMATH Keywords: nonlinear stability
zbMATH Keywords: logarithmic sensitivity
zbMATH Keywords: large perturbation
zbMATH Keywords: discontinuous data
MaRDI profile type: Publication
full work available at URL: j.jde.2018.04.041
OpenAlex ID: W2802099960
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DOI: 10.1016/J.JDE.2018.04.041
description: scientific article; zbMATH DE number 6875586