LEADER 04149nam 2200673 450 001 9910788741903321 005 20180613001307.0 010 $a1-4704-0456-7 035 $a(CKB)3360000000465036 035 $a(EBL)3114130 035 $a(SSID)ssj0000889258 035 $a(PQKBManifestationID)11549052 035 $a(PQKBTitleCode)TC0000889258 035 $a(PQKBWorkID)10876591 035 $a(PQKB)10991109 035 $a(MiAaPQ)EBC3114130 035 $a(RPAM)14226138 035 $a(PPN)195417402 035 $a(EXLCZ)993360000000465036 100 $a20060111h20062006 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTangential boundary stabilization of Navier-Stokes equations /$fViorel Barbu, Irena Lasiecka, Roberto Triggiani 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2006] 210 4$dİ2006 215 $a1 online resource (146 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 852 300 $a"Volume 181, number 852 (first of 5 numbers)." 311 $a0-8218-3874-1 320 $aIncludes bibliographical references. 327 $a""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*:Ha???(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 "" 327 $a""3.5. Theorem 2.1, general case d = 3: An infinite-dimensional opena???loop boundary controller g satisfying the FCC (3.1.22)a???(3.1.24) for the linearized systema???""""3.6. Feedback stabilization of the unstable [sub(Z)]Na???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 opena???loop boundary controller g satisfying the FCC ( 3.1.22)a???( 3.1.24) for the linearized systema???"" 327 $a""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)"" 327 $a""4.5. A Riccatia???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): Wella???posedness of the Naviera???Stokes equations with Riccatia???based boundary feedback control. Case d = 3 ""; ""Chapter 6. Theorem 2.3(ii): Local uniform stability of the Naviera???Stokes equations with Riccatia???based boundary feedback control""; ""Chapter 7. A PDEa???interpretation of the abstract results in Sections 5 and 6""; ""Appendix A. Technical Material Complementing Section 3.1"" 327 $a""B.3. Completion of the proof of Theorem 2.5 and Theorem 2.6 for the Na???S model (1.1), d = 2"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 852. 606 $aNavier-Stokes equations 606 $aBoundary layer 606 $aMathematical optimization 606 $aRiccati equation 615 0$aNavier-Stokes equations. 615 0$aBoundary layer. 615 0$aMathematical optimization. 615 0$aRiccati equation. 676 $a510 s 676 $a515/.353 700 $aBarbu$b Viorel$013745 702 $aLasiecka$b I$g(Irena),$f1948- 702 $aTriggiani$b R$g(Roberto),$f1942- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788741903321 996 $aTangential boundary stabilization of Navier-Stokes equations$93838120 997 $aUNINA