One-dimensional, non-local, first-order stationary mean-field games with congestion: A fourier approach

Levon Nurbekyan

doi:10.3934/dcdss.2018057

One-dimensional, non-local, first-order stationary mean-field games with congestion: A fourier approach

Levon Nurbekyan^*

^*Corresponding author for this work

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

8 Scopus citations

Abstract

Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric poly-nomials. Our technique is based on Fourier expansion methods.

Original language	English (US)
Pages (from-to)	963-990
Number of pages	28
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	11
Issue number	5
DOIs	https://doi.org/10.3934/dcdss.2018057
State	Published - Oct 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.

Keywords

Congestion
Fourier expansions
Non-local mean-field games

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdss.2018057

Cite this

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AB - Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric poly-nomials. Our technique is based on Fourier expansion methods.

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One-dimensional, non-local, first-order stationary mean-field games with congestion: A fourier approach

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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