Advances in Differential Equations

Self-similar blow up with a continuous range of values of the aggregated mass for a degenerate Keller-Segel system

Y. Sugiyama and J.J.L. Velázquez

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Abstract

In this paper we show that there exist radial solutions of the Keller-Segel system with porous medium like diffusion and critical exponents that blow up in a self-similar manner with a continuous range of masses. The situation is very different from the one that takes place for the usual Keller-Segel system with semilinear diffusion, that for critical nonlinearities yields blow up with a discrete set of values for the mass.

Article information

Source
Adv. Differential Equations Volume 16, Number 1/2 (2011), 85-112.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854331

Mathematical Reviews number (MathSciNet)
MR2766895

Zentralblatt MATH identifier
1221.35087

Subjects
Primary: 35K45: Initial value problems for second-order parabolic systems 35K57: Reaction-diffusion equations 35K65: Degenerate parabolic equations

Citation

Sugiyama, Y.; Velázquez, J.J.L. Self-similar blow up with a continuous range of values of the aggregated mass for a degenerate Keller-Segel system. Adv. Differential Equations 16 (2011), no. 1/2, 85--112. https://projecteuclid.org/euclid.ade/1355854331.


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