Large time behavior of averaged kinetic models on networks

Michael Herty; Christian Ringhofer

doi:10.1142/S0218202515500219

Large time behavior of averaged kinetic models on networks

Michael Herty
, Christian Ringhofer

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

2 Scopus citations

Abstract

We are interested in flows on general networks and derive a kinetic equation describing general production, social or transportation networks. Corresponding macroscopic transport equations for large time and homogenized behavior are obtained and studied numerically. This work continues a recent discussion [Averaged kinetic models for flows on unstructured networks, Kinetic Related Models 4 (2011) 1081-1096] and provides additionally explicit equilibrium solutions, second-order macroscopic approximations as well as numerical simulations on a large scale homogenized network. &Copy; 2015 World Scientific Publishing Company.

Original language	English (US)
Pages (from-to)	875-904
Number of pages	30
Journal	Mathematical Models and Methods in Applied Sciences
Volume	25
Issue number	5
DOIs	https://doi.org/10.1142/S0218202515500219
State	Published - May 25 2015

Keywords

Network dynamics
asymptotic analysis
kinetic theory

ASJC Scopus subject areas

Modeling and Simulation
Applied Mathematics

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10.1142/S0218202515500219

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title = "Large time behavior of averaged kinetic models on networks",

abstract = "We are interested in flows on general networks and derive a kinetic equation describing general production, social or transportation networks. Corresponding macroscopic transport equations for large time and homogenized behavior are obtained and studied numerically. This work continues a recent discussion [Averaged kinetic models for flows on unstructured networks, Kinetic Related Models 4 (2011) 1081-1096] and provides additionally explicit equilibrium solutions, second-order macroscopic approximations as well as numerical simulations on a large scale homogenized network. \&Copy; 2015 World Scientific Publishing Company.",

keywords = "Network dynamics, asymptotic analysis, kinetic theory",

author = "Michael Herty and Christian Ringhofer",

note = "Funding Information: The first author{\textquoteright}s work was supported by BMBF KinOpt, DFG Cluster of Excellence {\textquotedblleft}Production in High-Wage Countries{\textquotedblright} and DAAD 55866082. The second author{\textquoteright}s work was supported by KI-Net NSF RNMS Grant 11-07465.",

year = "2015",

month = may,

day = "25",

doi = "10.1142/S0218202515500219",

language = "English (US)",

volume = "25",

pages = "875--904",

journal = "Mathematical Models and Methods in Applied Sciences",

issn = "0218-2025",

publisher = "World Scientific Publishing Co. Pte Ltd",

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TY - JOUR

T1 - Large time behavior of averaged kinetic models on networks

AU - Herty, Michael

AU - Ringhofer, Christian

N1 - Funding Information: The first author’s work was supported by BMBF KinOpt, DFG Cluster of Excellence “Production in High-Wage Countries” and DAAD 55866082. The second author’s work was supported by KI-Net NSF RNMS Grant 11-07465.

PY - 2015/5/25

Y1 - 2015/5/25

N2 - We are interested in flows on general networks and derive a kinetic equation describing general production, social or transportation networks. Corresponding macroscopic transport equations for large time and homogenized behavior are obtained and studied numerically. This work continues a recent discussion [Averaged kinetic models for flows on unstructured networks, Kinetic Related Models 4 (2011) 1081-1096] and provides additionally explicit equilibrium solutions, second-order macroscopic approximations as well as numerical simulations on a large scale homogenized network. &Copy; 2015 World Scientific Publishing Company.

AB - We are interested in flows on general networks and derive a kinetic equation describing general production, social or transportation networks. Corresponding macroscopic transport equations for large time and homogenized behavior are obtained and studied numerically. This work continues a recent discussion [Averaged kinetic models for flows on unstructured networks, Kinetic Related Models 4 (2011) 1081-1096] and provides additionally explicit equilibrium solutions, second-order macroscopic approximations as well as numerical simulations on a large scale homogenized network. &Copy; 2015 World Scientific Publishing Company.

KW - Network dynamics

KW - asymptotic analysis

KW - kinetic theory

UR - https://www.scopus.com/pages/publications/84928410745

UR - https://www.scopus.com/pages/publications/84928410745#tab=citedBy

U2 - 10.1142/S0218202515500219

DO - 10.1142/S0218202515500219

M3 - Article

SN - 0218-2025

VL - 25

SP - 875

EP - 904

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 5

ER -

Large time behavior of averaged kinetic models on networks

Abstract

Keywords

ASJC Scopus subject areas

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