Nonlinear stability of diffusive contact wave for a chemotaxis model
type: Item
instance of: scholarly article
title: Nonlinear stability of diffusive contact wave for a chemotaxis model
zbMATH Open document ID: 1486.35042
author: Yanni Zeng
published in: Journal of Differential Equations
publication date: 2021-11-30T00:00:00Z
review text: The author considered the following initial value problem \begin{align*} &v_t+u_x=0,&& x\in \mathbb{R},t>0 \\ &u_t+(uv)_x=u_{xx}+ru(1-u),&& x\in \mathbb{R}, t>0, \\ &(v,u)(x,0)=(v_0,u_0)(x),&& x\in \mathbb{R}. \end{align*} The author studied Cauchy problem when the Cauchy data are near a diffusive contact wave, established global existence of solution and studied time asymptotic behavior of the solution. The author also obtained nonlinear stability of the diffusive contact wave. The result shows a significant difference when comparing the above model to Euler equations with damping.
reviewed by: Yuanyuan Ke
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 7436214
zbMATH Keywords: hyperbolic-parabolic balance laws
zbMATH Keywords: diffusive contact wave
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: logarithmic singularity
zbMATH Keywords: logistic growth
MaRDI profile type: Publication
full work available at URL: j.jde.2021.11.008
OpenAlex ID: W3214707017
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DOI: 10.1016/J.JDE.2021.11.008
description: scientific article; zbMATH DE number 7436214