Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension
type: Item
instance of: scholarly article
title: Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension
zbMATH Open document ID: 1505.35340
author: Youshan Tao
author: Michael Winkler
published in: Journal of Differential Equations
publication date: 2022-11-28T00:00:00Z
review text: The initial-boundary value problem with the homogeneous Neumann data for the chemotaxis-consumption system \begin{align*} u_t&=\Delta (u\phi(u)),\\ v_t&=\Delta v-uv, \end{align*} is considered in bounded smooth domains of \(\mathbb R^n\). A very weak-strong solution is constructed for diffusions with \(\phi(\xi)\sim \xi^{-\alpha}\). Regularity and long time asymptotic behavior of those solutions is studied for \(2\le n\le 5\), \(\alpha>\frac{n-2}{6-n}\), as well as for \(n=1\) under \(0<\phi\in C^3(0,\infty)\) assumption.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 7623963
zbMATH Keywords: chemotaxis
zbMATH Keywords: consumption
zbMATH Keywords: power-like diffusivity
zbMATH Keywords: weak-strong solution
MaRDI profile type: Publication
full work available at URL: j.jde.2022.10.022
OpenAlex ID: W4306987555
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DOI: 10.1016/J.JDE.2022.10.022
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description: scientific article; zbMATH DE number 7623963