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/

Zendy Plus

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

Zendy Tools

Zendy Open

In this paper, we analyze the dynamics of an $N$ particles system evolvingaccording the gradient flow of an energy functional. The particle system is aconsistent approximation of the Lagrangian formulation of a one parameterfamily of non-local drift-diffusion equations in one spatial dimension. Weshall prove the global in time existence of the trajectories of the particles(under a sufficient condition on the initial distribution) and give two blow-upcriteria. All these results are consequences of the competition between thediscrete entropy and the discrete interaction energy. They are also consistentwith the continuous setting, that in turn is a one dimension reformulation ofthe parabolic-elliptic Keller-Segel in high dimensions.

Blow-up dynamics of self-attracting diffusive particles driven by competing convexities