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

Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds

2021 ◽  
pp. 1-53
Author(s):  
Razvan C. Fetecau ◽  
Hansol Park ◽  
Francesco S. Patacchini
Keyword(s):  
Riemannian Manifolds ◽  
Collective Behavior ◽  
Mean Field ◽  
Sufficient Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
The Mean ◽  
Particle Approximation

We investigate a model for collective behavior with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure-valued solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle approximation. We study the long-time behavior of solutions to the model on sphere, where the primary goal is to establish sufficient conditions for a consensus state to form asymptotically. Well-posedness of solutions and the formation of consensus are also investigated for other manifolds (e.g., a hypercylinder).

Long-time behavior of quasistationary states of the Hamiltonian mean-field model

2007 ◽  
Vol 76 (4) ◽  
Author(s):  
Alessandro Campa ◽  
Andrea Giansanti ◽  
Gianluca Morelli
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Mean Field Model ◽  
Long Time

scholarly journals Asymptotic Behavior of Bounded Solutions to a First Order Gradient-like System

2019 ◽  
Vol 3 (1) ◽  
pp. 312
Author(s):  
Minh-Phuong Tran ◽  
Thanh-Nhan Nguyen
Keyword(s):  
Asymptotic Behavior ◽  
Original Work ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Bounded Solutions ◽  
First Order ◽  
Creative Commons ◽  
Convergence Results ◽  
Long Time ◽  
Open Access Article

In this paper, we prove the long time behavior of bounded solutions to a first order gradient-like system with low damping and perturbation terms. Our convergence results are obtained under some hypotheses of KurdykaLojasiewicz inequality and the angle and comparability condition.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

scholarly journals Long time behavior of a mean-field model of interacting neurons

2020 ◽  
Vol 130 (5) ◽  
pp. 2553-2595
Author(s):  
Quentin Cormier ◽  
Etienne Tanré ◽  
Romain Veltz
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Mean Field Model ◽  
Long Time

scholarly journals Long time behavior of the master equation in mean field game theory

2019 ◽  
Vol 12 (6) ◽  
pp. 1397-1453 ◽  
Author(s):  
Pierre Cardaliaguet ◽  
Alessio Porretta
Keyword(s):  
Game Theory ◽  
Master Equation ◽  
Mean Field ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Mean Field Game ◽  
Long Time

scholarly journals Pullback attractors via quasi-stability for non-autonomous lattice dynamical systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Radosław Czaja
Keyword(s):  
Dynamical Systems ◽  
Global Attractor ◽  
Exponential Attractor ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Pullback Attractors ◽  
Diffusion Operator ◽  
First Order ◽  
Lattice Dynamical Systems ◽  
Long Time

<p style='text-indent:20px;'>In this paper we study long-time behavior of first-order non-autono-mous lattice dynamical systems in square summable space of double-sided sequences using the cooperation between the discretized diffusion operator and the discretized reaction term. We obtain existence of a pullback global attractor and construct pullback exponential attractor applying the introduced notion of quasi-stability of the corresponding evolution process.</p>

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