Some controllability results for linear viscoelastic fluids

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...

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Detalhes bibliográficos
Autores: Boldrini, José Luiz, Doubova Krasotchenko, Anna, Fernández Cara, Enrique, González Burgos, Manuel
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41191
Acesso em linha:http://hdl.handle.net/11441/41191
https://doi.org/10.1137/100813592
Access Level:acceso abierto
Palavra-chave:Controllability
Maxwell fluids
Viscoelastic fluids
Descrição
Resumo: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.