Phase transitions and bump solutions of the keller-segel model with volume exclusion

Jose A. Carrillo; Xinfu Chen; Qi Wang; Zhian Wang; Lu Zhang

doi:10.1137/19M125827X

Phase transitions and bump solutions of the keller-segel model with volume exclusion

Jose A. Carrillo, Xinfu Chen, Qi Wang, Zhian Wang, Lu Zhang

Research output: Journal article publication › Journal article › Academic research › peer-review

11 Citations (Scopus)

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.

Original language	English
Pages (from-to)	232-261
Number of pages	30
Journal	SIAM Journal on Applied Mathematics
Volume	80
Issue number	1
DOIs	https://doi.org/10.1137/19M125827X
Publication status	Published - 16 Jan 2020

Keywords

Bifurcation
Bump solution
Degenerate diffusion
Keller-Segel
Phase transition

ASJC Scopus subject areas

Applied Mathematics

More information

10.1137/19M125827X

Cite this

@article{975343ddf1d249a29f8cbaf49f16a514,

title = "Phase transitions and bump solutions of the keller-segel model with volume exclusion",

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.",

keywords = "Bifurcation, Bump solution, Degenerate diffusion, Keller-Segel, Phase transition",

author = "Carrillo, {Jose A.} and Xinfu Chen and Qi Wang and Zhian Wang and Lu Zhang",

year = "2020",

month = jan,

day = "16",

doi = "10.1137/19M125827X",

language = "English",

volume = "80",

pages = "232--261",

journal = "SIAM Journal on Applied Mathematics",

issn = "0036-1399",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - Phase transitions and bump solutions of the keller-segel model with volume exclusion

AU - Carrillo, Jose A.

AU - Chen, Xinfu

AU - Wang, Qi

AU - Wang, Zhian

AU - Zhang, Lu

PY - 2020/1/16

Y1 - 2020/1/16

N2 - 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.

AB - 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.

KW - Bifurcation

KW - Bump solution

KW - Degenerate diffusion

KW - Keller-Segel

KW - Phase transition

UR - http://www.scopus.com/inward/record.url?scp=85079737616&partnerID=8YFLogxK

U2 - 10.1137/19M125827X

DO - 10.1137/19M125827X

M3 - Journal article

AN - SCOPUS:85079737616

SN - 0036-1399

VL - 80

SP - 232

EP - 261

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 1

ER -

Phase transitions and bump solutions of the keller-segel model with volume exclusion

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this