04152nam 2200673 450 991048040050332120180613001307.01-4704-0456-7(CKB)3360000000465036(EBL)3114130(SSID)ssj0000889258(PQKBManifestationID)11549052(PQKBTitleCode)TC0000889258(PQKBWorkID)10876591(PQKB)10991109(MiAaPQ)EBC3114130(PPN)195417402(EXLCZ)99336000000046503620060111h20062006 uy| 0engur|n|---|||||txtccrTangential boundary stabilization of Navier-Stokes equations /Viorel Barbu, Irena Lasiecka, Roberto TriggianiProvidence, Rhode Island :American Mathematical Society,[2006]©20061 online resource (146 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 852"Volume 181, number 852 (first of 5 numbers)."0-8218-3874-1 Includes bibliographical references.""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 openâ€?loop boundary controller g satisfying the FCC (3.1.22)â€?(3.1.24) for the linearized systemâ€?""""3.6. Feedback stabilization of the unstable [sub(Z)]Nâ€?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 openâ€?loop boundary controller g satisfying the FCC ( 3.1.22)â€?( 3.1.24) for the linearized systemâ€?""""Chapter 4. Boundary feedback uniform stabilization of the linearized system( 3.1.4) via an optimal control problem and corresponding 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 Riccatiâ€?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): Wellâ€?posedness of the Navierâ€?Stokes equations with Riccatiâ€?based boundary feedback control. Case d = 3 ""; ""Chapter 6. Theorem 2.3(ii): Local uniform stability of the Navierâ€?Stokes equations with Riccatiâ€?based boundary feedback control""; ""Chapter 7. A PDEâ€?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 Nâ€?S model (1.1), d = 2""Memoirs of the American Mathematical Society ;no. 852.Navier-Stokes equationsBoundary layerMathematical optimizationRiccati equationElectronic books.Navier-Stokes equations.Boundary layer.Mathematical optimization.Riccati equation.510 s515/.353Barbu Viorel13745Lasiecka I(Irena),1948-Triggiani R(Roberto),1942-MiAaPQMiAaPQMiAaPQBOOK9910480400503321Tangential boundary stabilization of Navier-Stokes equations2175520UNINA