2009
DOI: 10.1016/j.sysconle.2009.02.010
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Riccati theory and singular estimates for a Bolza control problem arising in linearized fluid–structure interaction

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Cited by 35 publications
(55 citation statements)
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“…For the fluid-structure interaction under investigation, which comprises a parabolic and a hyperbolic PDE, it was shown in [26] that a singular estimate (for the corresponding abstract evolution) is satisfied in the finite energy space, as long as the penalization in the quadratic functional does not involve the mechanical energy at a truly energy level. More precisely, the study in [26] established specific singular estimates and hence well-posedness of the Riccati equations in the special case of penalization of the mechanical variables below the energy level (say, sub-critical penalization), yet allowing full penalization of the fluid variable.…”
mentioning
confidence: 99%
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“…For the fluid-structure interaction under investigation, which comprises a parabolic and a hyperbolic PDE, it was shown in [26] that a singular estimate (for the corresponding abstract evolution) is satisfied in the finite energy space, as long as the penalization in the quadratic functional does not involve the mechanical energy at a truly energy level. More precisely, the study in [26] established specific singular estimates and hence well-posedness of the Riccati equations in the special case of penalization of the mechanical variables below the energy level (say, sub-critical penalization), yet allowing full penalization of the fluid variable.…”
mentioning
confidence: 99%
“…More precisely, the study in [26] established specific singular estimates and hence well-posedness of the Riccati equations in the special case of penalization of the mechanical variables below the energy level (say, sub-critical penalization), yet allowing full penalization of the fluid variable.…”
mentioning
confidence: 99%
“…> 0 , does not require any smoothing property imposed on the observation operator R. In fact, one can also consider unbounded observation (eg first order differential operator in the Neumann case). This is in contrast with other treatments where such smoothing was required [25,35,36].…”
Section: Remark 54mentioning
confidence: 80%
“…s . The second approach, instead, is variational: it was presented in [33][34][35][36]. We shall use this approach here.…”
Section: Specialization Of Abstract Model To the Fluidstructure Intermentioning
confidence: 99%
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