Blowup behavior of solutions to the rescaled Jäger-Luckhaus system.
type: Item
instance of: scholarly article
title: Blowup behavior of solutions to the rescaled Jäger-Luckhaus system.
zbMATH Open document ID: 1035.35007
author: Takasi Senba
author: Takashi Suzuki
published in: Advances in Differential Equations
publication date: 2003-11-10T00:00:00Z
review text: The Jäger-Luckhaus system was introduced by Jäger and Luckhaus for the purpose of modeling chemotaxis. The Jäger-Luckhaus system consists of partial differential equations of parabolic and elliptic types, and the behavior of its solutions depends on a parameter \(\lambda\), which in turn is related to the \(L^1\)-norm of the initial datum. When \(\lambda\ll 1\), the solutions of the Jäger-Luckhaus system exist for all time. In contrast, its solutions associated with \(\lambda\gg 1\) blow up in a finite time. In this paper, the authors rescale the Jäger-Luckhaus system around the blowup points and study the infinite time blowup behavior of the rescaled system. They show that the solutions of the rescaled system converge to a sum of functions with support concentrated at the blowup points and with integral equal to \(8\pi\) (for blowup points inside the domain) or \(4\pi\) (for blowup points on the boundary). The interpretation of this result is that the quantization of chemotactic collapse occurs. The proof is very technical and is divided into a major proposition and several lemmas.
reviewed by: Jiahong Wu
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 2002549
zbMATH Keywords: quantization of chemotactic collapse
zbMATH Keywords: infinite time blowup
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2002549