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• W2963705414 abstract "We study the asymptotic behavior, as time variable t goes to +∞, of nonautonomous dynamical systems involving multiscale features. As a benchmark case, given H a general Hilbert space, Φ:H→R∪{+∞} and Ψ:H→R∪{+∞} two closed convex functions, and β a function of t which tends to +∞ as t goes to +∞, we consider the differential inclusionx˙(t)+∂Φ(x(t))+β(t)∂Ψ(x(t))∋0. 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. As a key ingredient we assume that, for every p belonging to the range of NC∫0+∞β(t)[Ψ∗(pβ(t))−σC(pβ(t))]dt<+∞ where Ψ∗ is the Fenchel conjugate of Ψ, σC is the support function of C=argminΨ and NC(x) is the normal cone to C at x. As a by-product, we revisit the systemx˙(t)+ϵ(t)∂Φ(x(t))+∂Ψ(x(t))∋0 where ϵ(t) tends to zero as t goes to +∞ and ∫0+∞ϵ(t)dt=+∞, whose asymptotic behavior can be derived from the preceding one by time rescaling. Applications are given in game theory, optimal control, variational problems and PDEs." @default.
• W2963705414 created "2019-07-30" @default.
• W2963705414 creator A5038818485 @default.
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• W2963705414 date "2010-03-01" @default.
• W2963705414 modified "2023-10-16" @default.
• W2963705414 title "Asymptotic behavior of coupled dynamical systems with multiscale aspects" @default.
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• W2963705414 doi "https://doi.org/10.1016/j.jde.2009.06.014" @default.
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