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Asymptotic equivalence and Kobayashi-type estimates for nonautonomous monotone operators in Banach spaces

F Alvarez (falvarez***at***dim.uchile.cl)
J Peypouquet (juan.peypouquet***at***usm.cl)

Abstract: We provide a sharp generalization to the nonautonomous case of the well-known Ko\-ba\-yashi estimate for proximal iterates associated with maximal monotone operators. We then derive a bound for the distance between a continuous-in-time trajectory, namely the solution to the differential inclusion $\dot{x} + A(t)x\ni 0$, and the corresponding proximal iterations. We also establish continuity properties with respect to time of the nonautonomous flow under simple assumptions by revealing their link with the function $t\mapsto A(t)$. Moreover, our sharper estimations allow us to derive equivalence results which are useful to compare the asymptotic behavior of the trajectories defined by different evolution systems. We do so by extending a classical result of Passty to the nonautonomous setting.

Keywords: Monotone operators, evolution equations, Koayashi-type estimates

Category 1: Applications -- Science and Engineering (Basic Sciences Applications )

Citation: Unpublished, UTFSM-CMM, Chile 2008

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Entry Submitted: 05/13/2008
Entry Accepted: 05/13/2008
Entry Last Modified: 04/20/2009

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