English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We investigate the one-dimensional Keller-Segel model where the diffusion isreplaced by a non-local operator, namely the fractional diffusion with exponent$0<\alpha\leq 2$. We prove some features related to the classicaltwo-dimensional Keller-Segel system: blow-up may or may not occur depending onthe initial data. More precisely a singularity appears in finite time when$\alpha<1$ and the initial configuration of cells is sufficiently concentrated.On the opposite, global existence holds true for $\alpha\leq1$ if the initialdensity is small enough in the sense of the $L^{1/\alpha}$ norm.

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