A relaxation result for state constrained inclusions in infinite dimension | Zendy

Hélène Frankowska | Zendy; Elsa M. Marchini | Zendy; Marco Mazzola | Zendy

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A relaxation result for state constrained inclusions in infinite dimension

Author(s) -

Hélène Frankowska,

Elsa M. Marchini,

Marco Mazzola

Publication year - 2016

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2016.6.113

Subject(s) - differential inclusion , banach space , separable space , dimension (graph theory) , generator (circuit theory) , mathematics , relaxation (psychology) , state (computer science) , constraint (computer aided design) , semigroup , set (abstract data type) , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , physics , quantum mechanics , computer science , geometry , algorithm , psychology , social psychology , power (physics) , programming language

International audienceIn 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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