Type II blowup of solutions to a simplified Keller-Segel system in two dimensional domains
type: Item
instance of: scholarly article
title: Type II blowup of solutions to a simplified Keller-Segel system in two dimensional domains
zbMATH Open document ID: 1114.35090
author: Takasi Senba
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-04-13T00:00:00Z
review text: The following problem to the Keller-Segel system \[ \begin{aligned} \left.\begin{aligned} u_t&=\nabla(\nabla u-u \nabla u)\\ 0&=\Delta v-v+u\end{aligned} \right\} \quad &\text{in }\Omega,\\ \frac{\partial u}{\partial \nu }= \frac{\partial v}{\partial \nu }=0 \quad &\text{on } \partial \Omega,\\ u(\cdot,0)=u_0 \quad &\text{in } \Omega,\end{aligned} \] is considered. Here \(\Omega\) is a bounded domain in \(\mathbb R^2\) with smooth boundary \(\partial \Omega, \nu =\nu (x)\) in the unit normal outer vector on \(\partial \Omega\), and \(u_0\) is smooth and non-negative in \(\overline{\Omega}\). The author investigates whether finite time blowup solutions to the system exhibit Type II blowup or not. It is shown existing of the radial solution whose blowup speed is faster than that of backward self similar solution.
reviewed by: Mersaid Aripov
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 5142234
zbMATH Keywords: Keller-Segel system
zbMATH Keywords: blowup
zbMATH Keywords: type II
zbMATH Keywords: solution
zbMATH Keywords: parabolic-elliptic system
zbMATH Keywords: radial solution
zbMATH Keywords: backward self similar solution
MaRDI profile type: Publication
full work available at URL: j.na.2006.02.027
OpenAlex ID: W2095244803
cites work: Q4398321
cites work: Initiation of slime mold aggregation viewed as an instability
cites work: Q4872331
cites work: Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
cites work: Chemotactic collapse in a parabolic-elliptic system of mathematical biology
cites work: Parabolic system of chemotaxis: Blowup in a finite and the infinite time.
cites work: Blowup behavior of solutions to the rescaled Jäger-Luckhaus system.
cites work: Free energy and self-interacting particles
DOI: 10.1016/J.NA.2006.02.027
description: scientific article; zbMATH DE number 5142234