The one-dimensional Keller-Segel model with fractional diffusion of cells

Nikolaos Bournaveas, Vincent Calvez

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent 0 < alpha <= 2. We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data. More precisely a singularity appears in finite time when alpha < 1 and the initial configuration of cells is sufficiently concentrated. On the other hand, global existence holds true for alpha <= 1 if the initial density is small enough in the sense of the L-1/alpha norm.

Original languageEnglish
Pages (from-to)923-935
Number of pages13
JournalNonlinearity
Volume23
Issue number4
DOIs
Publication statusPublished - Apr 2010

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