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Some controllability results for linear viscoelastic fluids


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Opened Access Some controllability results for linear viscoelastic fluids

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Author: Boldrini, José Luiz
Doubova Krasotchenko, Anna
Fernández Cara, Enrique
González Burgos, Manuel
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2012
Published in: SIAM Journal on Control and Optimization, 50(2), 900-924
Document type: Article
Abstract: We analyze the controllability properties of systems which provide a description, at first approximation, of a kind of viscoelastic fluid. We consider linear Maxwell fluids. First, we establish the large time approximate-finite dimensional controllability of the system, with distributed or boundary controls supported by arbitrary small sets. Then, we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets. The proofs of these results rely on classical arguments. In particular, the approximate controllability result is implied by appropriate unique continuation properties, while exact controllability is a consequence of observability (inverse) inequalities. We also discuss questions concerning the controllability of viscoelastic fluids and some related open problems.
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