Prevention of infinite-time blowup by slightly super-linear degradation in a Keller–Segel system with density-suppressed motility

An initial-Neumann boundary value problem for a Keller–Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension N ⩾ 2 . In this work, we prove that with any source t...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinearity 2024-09, Vol.37 (9), p.95007
Main Authors: Xiao, Yamin, Jiang, Jie
Format: Article
Language:English
Subjects:
35A01
35K51
35K55
boundedness
chemotaxis
classical solution
comparison
degradation
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An initial-Neumann boundary value problem for a Keller–Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension N ⩾ 2 . In this work, we prove that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of s log ⁡ s at most, the classical solution is uniformly-in-time bounded when N ⩽ 3 , thus preventing the infinite-time explosion detected in the source-free counter-part. The cornerstone of our proof lies in an improved comparison argument and a construction of an entropy inequality.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ad6113