Differential and Integral Equations

Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems

Yoshie Sugiyama

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We consider the degenerate Keller-Segel system (KS) of Nagai type below. We prove that when $m > 2-\frac{2}{N}$, the problem (KS) is solvable globally in time without any restriction on the size of the initial data and that when $1 < m \le 2-\frac{2}{N}$, the problem (KS) evolves in a finite time blow-up for some large initial data. Hence, we completely classify the existence and non-existence of the time global solution by means of the exponent $m=2-\frac{2}{N}$, which generalizes the Fujita exponent for (KS).

Article information

Source
Differential Integral Equations, Volume 19, Number 8 (2006), 841-876.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050338

Mathematical Reviews number (MathSciNet)
MR2263432

Zentralblatt MATH identifier
1212.35240

Subjects
Primary: 35K45: Initial value problems for second-order parabolic systems
Secondary: 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations 92C17: Cell movement (chemotaxis, etc.)

Citation

Sugiyama, Yoshie. Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems. Differential Integral Equations 19 (2006), no. 8, 841--876. https://projecteuclid.org/euclid.die/1356050338


Export citation