Phase transitions and bump solutions of the Keller-Segel model with volume exclusion
File(s)SIAP-submitted.pdf (791.35 KB)
Accepted version
Author(s)
Carrillo de la Plata, Jose Antonio
Chen, Xinfu
Wang, Qi
Wang, Zhian
Zhang, Lu
Type
Journal Article
Abstract
We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myriad of symmetric and asymmetric stationary states whose stability properties are mostly studied via free energy decreasing numerical schemes. The metastability behavior and staircased free energy decay are also illustrated via these numerical simulations.
Date Issued
2020-01-16
Date Acceptance
2019-10-28
Citation
SIAM Journal on Applied Mathematics, 2020, 80 (1), pp.232-261
ISSN
0036-1399
Publisher
Society for Industrial and Applied Mathematics
Start Page
232
End Page
261
Journal / Book Title
SIAM Journal on Applied Mathematics
Volume
80
Issue
1
Copyright Statement
© 2020, Society for Industrial and Applied Mathematics.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://epubs.siam.org/doi/10.1137/19M125827X
Grant Number
EP/P031587/1
Subjects
0102 Applied Mathematics
Applied Mathematics
Publication Status
Published
Date Publish Online
2020-01-16