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A relaxation result for state constrained inclusions in infinite dimension

Abstract : In this paper we consider a state constrained differential inclusion ˙ x ∈ Ax + F (t, x), with A generator of a strongly continuous semigroup in an infinite dimensional separable Banach space. Under an "inward pointing condition" we prove a relaxation result stating that the set of trajectories lying in the interior of the constraint is dense in the set of constrained trajectories of the convexified inclusion ˙ x ∈ Ax + coF (t, x). Some applications to control problems involving PDEs are given.
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Submitted on : Thursday, January 1, 2015 - 5:46:44 PM
Last modification on : Thursday, December 10, 2020 - 12:31:35 PM
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Hélène Frankowska, Elsa Marchini, Marco Mazzola. A relaxation result for state constrained inclusions in infinite dimension. Mathematical Control and Related Fields, AIMS, 2015, 6 (1), pp.113-141. ⟨10.3934/mcrf.2016.6.113⟩. ⟨hal-01099223⟩

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