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Record Nr. |
UNINA9910480400503321 |
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Autore |
Barbu Viorel |
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Titolo |
Tangential boundary stabilization of Navier-Stokes equations / / Viorel Barbu, Irena Lasiecka, Roberto Triggiani |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [2006] |
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©2006 |
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ISBN |
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Descrizione fisica |
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1 online resource (146 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 852 |
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Disciplina |
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Soggetti |
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Navier-Stokes equations |
Boundary layer |
Mathematical optimization |
Riccati equation |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"Volume 181, number 852 (first of 5 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""Contents""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""Chapter 2. Main results""; ""Chapter 3. Proof of Theorems 2.1 and 2.2 on the linearized system ( 2.4): d = 3""; ""3.1. Abstract models of the linearized problem ( 2.3). Regularity ""; ""3.2. The operator D*A, D*:Hâ??(L[sup(2)](T))[sub(D)]""; ""3.3. A critical boundary property related to the boundary c.c. in ( 3.1.2e) ""; ""3.4. Some technical preliminaries; space and system decomposition "" |
""3.5. Theorem 2.1, general case d = 3: An infinite-dimensional open�loop boundary controller g satisfying the FCC (3.1.22)�(3.1.24) for the linearized system�""""3.6. Feedback stabilization of the unstable [sub(Z)]N�system ( 3.4.9) on Z[sup(u)][sub(N)] under the FDSA""; ""3.7. Theorem 2.2, case d = 3 under the FDSA: An open�loop boundary controller g satisfying the FCC ( 3.1.22)�( 3.1.24) for the linearized system�"" |
""Chapter 4. Boundary feedback uniform stabilization of the linearized system( 3.1.4) via an optimal control problem and corresponding |
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Riccati theory. Case d = 3""""4.0. Orientation""; ""4.1. The optimal control problem ( Case d = 3)""; ""4.2. Optimal feedback dynamics: the feedback semigroup and its generator on W""; ""4.3. Feedback synthesis via the Riccati operator""; ""4.4. Identification of the Riccati operator R in ( 4.1.8) with the operator R[sub(1)] in ( 4.3.1)"" |
""4.5. A Riccati�type algebraic equation satisfied by the operator R on the domain D(A[sup2)][Sub(R)], Where A[sub(R)] is the feedback generator""""Chapter 5. Theorem 2.3(i): Well�posedness of the Navier�Stokes equations with Riccati�based boundary feedback control. Case d = 3 ""; ""Chapter 6. Theorem 2.3(ii): Local uniform stability of the Navier�Stokes equations with Riccati�based boundary feedback control""; ""Chapter 7. A PDE�interpretation of the abstract results in Sections 5 and 6""; ""Appendix A. Technical Material Complementing Section 3.1"" |
""B.3. Completion of the proof of Theorem 2.5 and Theorem 2.6 for the N�S model (1.1), d = 2"" |
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