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

2018 ◽  
Vol 11 (5) ◽  
pp. 963-990 ◽  
Author(s):  
Levon Nurbekyan ◽  
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
One Dimensional ◽  
First Order ◽  
Non Local

scholarly journals Long-Time Behavior of First-Order Mean Field Games on Euclidean Space

2019 ◽  
Vol 10 (2) ◽  
pp. 361-390
Author(s):  
Piermarco Cannarsa ◽  
Wei Cheng ◽  
Cristian Mendico ◽  
Kaizhi Wang
Keyword(s):  
Euclidean Space ◽  
Mean Field ◽  
Mean Field Games ◽  
Time Behavior ◽  
Long Time Behavior ◽  
First Order ◽  
Long Time

scholarly journals First-order, stationary mean-field games with congestion

2018 ◽  
Vol 173 ◽  
pp. 37-74 ◽  
Author(s):  
David Evangelista ◽  
Rita Ferreira ◽  
Diogo A. Gomes ◽  
Levon Nurbekyan ◽  
Vardan Voskanyan
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
First Order

scholarly journals Viability analysis of the first-order mean field games

2020 ◽  
Vol 26 ◽  
pp. 33
Author(s):  
Yurii Averboukh
Keyword(s):  
Mean Field ◽  
Initial Distribution ◽  
Initial Time ◽  
Mean Field Games ◽  
Sufficient Condition ◽  
Mean Field Game ◽  
First Order ◽  
Viability Analysis ◽  
A Value ◽  
Object Of Study

In the paper, we examine the dependence of the solution of the deterministic mean field game on the initial distribution of players. The main object of study is the mapping which assigns to the initial time and the initial distribution of players the set of expected rewards of the representative player corresponding to solutions of mean field game. This mapping can be regarded as a value multifunction. We obtain the sufficient condition for a multifunction to be a value multifunction. It states that if a multifunction is viable with respect to the dynamics generated by the original mean field game, then it is a value multifunction. Furthermore, the infinitesimal variant of this condition is derived.

scholarly journals The selection problem for some first-order stationary Mean-field games

2020 ◽  
Vol 15 (4) ◽  
pp. 681-710
Author(s):  
Diogo A. Gomes ◽  
◽  
Hiroyoshi Mitake ◽  
Kengo Terai ◽  
Keyword(s):  
Mean Field ◽  
Selection Problem ◽  
Mean Field Games ◽  
First Order

scholarly journals On the magnetorotational instability and elastic buckling

2015 ◽  
Vol 471 (2177) ◽  
pp. 20140699 ◽  
Author(s):  
Geoffrey M. Vasil
Keyword(s):  
Mean Field ◽  
Elastic Beam ◽  
Nonlinear Feedback ◽  
Magnetorotational Instability ◽  
Universal Class ◽  
Dynamical Equations ◽  
One Dimensional ◽  
Elastic Systems ◽  
Non Local ◽  
Asymptotic Reduction

This paper demonstrates an equivalence between rotating magnetized shear flows and a stressed elastic beam. This results from finding the same form of dynamical equations after an asymptotic reduction of the axis-symmetric magnetorotational instability (MRI) under the assumption of almost-critical driving. The analysis considers the MRI dynamics in a non-dissipative near-equilibrium regime. Both the magnetic and elastic systems reduce to a simple one-dimensional wave equation with a non-local nonlinear feedback. Under transformation, the equation comprises a large number of mean-field interacting Duffing oscillators. This system was the first proven example of a strange attractor in a partial differential equation. Finding the same reduced equation in two natural applications suggests the model might result from other applications and could fall into a universal class based on symmetry.

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