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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An initial-Neumann boundary value problem for a Keller--Segel system withdensity-suppressed motility and source terms is considered. Infinite-timeblowup of the classical solution was previously observed for its source-freeversion when dimension $N\geq2$. In this work, we prove that with any sourceterm involving a slightly super-linear degradation effect on the density, of agrowth order of $s\log s$ at most, the classical solution is uniformly-in-timebounded when $N\leq3$, thus preventing the infinite-time explosion detected inthe source-free counter-part. The cornerstone of our proof lies in an improvedcomparison argument and a construction of an entropy inequality.

Prevention of Infinite-time Blowup by Slightly Super-linear Degradation in a Keller--Segel System with Density-suppressed Motility