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Some controllability results for linear viscoelastic fluids. (English) Zbl 1244.93022
Summary: 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.
MSC:
93B05Controllability
35Q35PDEs in connection with fluid mechanics
76A10Viscoelastic fluids
76D55Flow control and optimization
93C20Control systems governed by PDE