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Asymptotic behavior of coupled dynamical systems with multiscale aspects
Journal article   Open access   Peer reviewed

Asymptotic behavior of coupled dynamical systems with multiscale aspects

Hedy Attouch and Marc-Olivier Czarnecki
Journal of Differential Equations, Vol.248(6), pp.1315-1344
15/03/2010
DOI: https://doi.org/10.1016/j.jde.2009.06.014

Abstract

Nonautonomous gradient-like systems Monotone inclusions Asymptotic behavior Time multiscaling Convex minimization Hierarchical optimization Asymptotic control Slow control Potential games Best response Splitting methods Domain decomposition for PDEs
We study the asymptotic behavior, as time variable t goes to infinity, of nonautonomous dynamical systems involving multiscale features. This system models the emergence of various collective behaviors in game theory, as well as the asymptotic control of coupled systems. We show several results ranging from weak ergodic to strong convergence of the trajectories.
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