Threshold for shock formation in the hyperbolic Keller-Segel model

Yongki Lee; Hailiang Liu

doi:10.1016/j.aml.2015.06.001

Threshold for shock formation in the hyperbolic Keller-Segel model

Yongki Lee, Hailiang Liu

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We identify a sub-threshold for finite time shock formation in solutions to the one-dimensional hyperbolic Keller-Segel model. The main result states that under some assumptions on the initial potential, if the slope of the initial density is above a threshold at even one location, the solution must become discontinuous in finite time.

Original language	English
Article number	4802
Pages (from-to)	56-63
Number of pages	8
Journal	Applied Mathematics Letters
Volume	50
DOIs	https://doi.org/10.1016/j.aml.2015.06.001
State	Published - Jun 27 2015

Scopus Subject Areas

Applied Mathematics

Keywords

Critical threshold
Keller-Segel model
Nonlocal conservation law
Shock formation
Traffic flow

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10.1016/j.aml.2015.06.001

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title = "Threshold for shock formation in the hyperbolic Keller-Segel model",

abstract = "We identify a sub-threshold for finite time shock formation in solutions to the one-dimensional hyperbolic Keller-Segel model. The main result states that under some assumptions on the initial potential, if the slope of the initial density is above a threshold at even one location, the solution must become discontinuous in finite time.",

keywords = "Critical threshold, Keller-Segel model, Nonlocal conservation law, Shock formation, Traffic flow",

author = "Yongki Lee and Hailiang Liu",

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year = "2015",

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AU - Liu, Hailiang

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N2 - We identify a sub-threshold for finite time shock formation in solutions to the one-dimensional hyperbolic Keller-Segel model. The main result states that under some assumptions on the initial potential, if the slope of the initial density is above a threshold at even one location, the solution must become discontinuous in finite time.

AB - We identify a sub-threshold for finite time shock formation in solutions to the one-dimensional hyperbolic Keller-Segel model. The main result states that under some assumptions on the initial potential, if the slope of the initial density is above a threshold at even one location, the solution must become discontinuous in finite time.

KW - Critical threshold

KW - Keller-Segel model

KW - Nonlocal conservation law

KW - Shock formation

KW - Traffic flow

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DO - 10.1016/j.aml.2015.06.001

M3 - Article

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VL - 50

SP - 56

EP - 63

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 4802

ER -

Threshold for shock formation in the hyperbolic Keller-Segel model

Abstract

Scopus Subject Areas

Keywords

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