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

Y. Sugiyama; J. J.L. Velázquez

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

Y. Sugiyama, 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.

Original language	English
Pages (from-to)	85-112
Number of pages	28
Journal	Advances in Differential Equations
Volume	16
Issue number	1-2
Publication status	Published - 2011
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Cite this

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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.",

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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