Trajectories of differential inclusions with state constraints

Alberto Bressan, Giancarlo Facchi

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Abstract

The paper deals with solutions of a differential inclusion ẋ∈ F(x) constrained to a compact convex set Ω. Here F is a compact, possibly non-convex valued, Lipschitz continuous multifunction, whose convex closure coF satisfies a strict inward pointing condition at every boundary point x∈∂Ω. Given a reference trajectory x*(·) taking values in an ε-neighborhood of Ω, we prove the existence of a second trajectory x:[0,T]→Ω which satisfies ||x-x*||W1,1{less-than above slanted equal above greater-than above slanted equal}Cε(1+|lnε|). As shown by an earlier counterexample, this bound is sharp.

Original languageEnglish (US)
Pages (from-to)2267-2281
Number of pages15
JournalJournal of Differential Equations
Volume250
Issue number4
DOIs
StatePublished - Feb 15 2011

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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