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October  2018, 11(5): 963-990. doi: 10.3934/dcdss.2018057

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

 4700 King Abdullah University of Science and Technology, CEMSE Division, Thuwal, 23955-6900, KSA

Received  March 2017 Revised  September 2017 Published  June 2018

Fund Project: The author is supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering.

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 polynomials. Our technique is based on Fourier expansion methods.

Citation: Levon Nurbekyan. One-dimensional, non-local, first-order stationary mean-field games with congestion: A Fourier approach. Discrete & Continuous Dynamical Systems - S, 2018, 11 (5) : 963-990. doi: 10.3934/dcdss.2018057
##### References:

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##### References:
The kernel G1 and the potential V.
The approximate solutions $\widetilde{m}_1$ and $\widetilde{u}_1$.
The error Er1.
The kernel G2 and the potential V.
The approximate solutions $\widetilde{m}_2$ and $\widetilde{u}_2$.
The error Er2.
The kernel G3 and the potential V.
The approximate solutions $\widetilde{m}_3$ and $\widetilde{u}_3$.
The error Er3.
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