Paper Info
Title
Mass Threshold For Infinite-Time Blowup In A Chemotaxis Model With Split Population
Abstract
We study a chemotaxis model describing the space and time evolution in a smooth and bounded domain of R-2 of the densities u and v of subpopulations of moving and static individuals of some species and the concentration w of a chemoattractant. We prove that, in an appropriate functional setting, all solutions exist globally in time. Moreover, we establish the existence of a critical mass M-c > 0 of the whole population u + v such that, for M is an element of (0, M-c), any solution is bounded, while, for almost all M > M-c, there exist solutions blowing up in infinite time. The building block of the analysis is the construction of a Liapunov functional. As far as we know, this is the first result of this kind when the mass conservation includes the two subpopulations and not only the moving one.
Year
DOI
Venue
2021
10.1137/20M1371968
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
DocType
Volume
chemotaxis system, species with two subpopulations, global solutions, critical mass, infinite-time blowup
Journal
53
Issue
ISSN
Citations 
3
0036-1410
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Philippe Laurençot13010.30
Christian Stinner272.13