LEADER 05659nam 2200709 a 450 001 9910457497603321 005 20200520144314.0 010 $a981-4366-89-7 035 $a(CKB)2550000000087658 035 $a(EBL)846124 035 $a(SSID)ssj0000735352 035 $a(PQKBManifestationID)11378060 035 $a(PQKBTitleCode)TC0000735352 035 $a(PQKBWorkID)10749952 035 $a(PQKB)10344415 035 $a(MiAaPQ)EBC846124 035 $a(WSP)00008267 035 $a(Au-PeEL)EBL846124 035 $a(CaPaEBR)ebr10529361 035 $a(CaONFJC)MIL498439 035 $a(OCoLC)785777960 035 $a(EXLCZ)992550000000087658 100 $a20120227d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMultiscale problems$b[electronic resource] $etheory, numerical approximation and applications /$feditors, Alain Damlamian, Bernadette Miara, Tatsien Li 210 $aBeijing, China $cHigher Education Press$d2011 215 $a1 online resource (314 p.) 225 1 $aSeries in contemporary applied mathematics ;$v16 300 $aDescription based upon print version of record. 311 $a981-4366-88-9 320 $aIncludes bibliographical references. 327 $aPreface; Contents; Alain Damlamian An Introduction to Periodic Homogenization; 1 Introduction; 2 The main ideas of Homogenization; The three steps of Homogenization; 3 The model problem and three theoretical methods; 3.1 The multiple-scale expansion method; 3.2 The oscillating test functions method; 3.2.1 The proof of Theorem 3.4; 3.2.2 Convergence of the energy; 3.3 The two-scale convergence method; References; Alain Damlamian The Periodic Unfolding Method in Homogenization; 1 Introduction; 2 Unfolding in Lp-spaces; 2.1 The unfolding operator T; 2.2 The averaging operator U 327 $a2.3 The connection with two-scale convergence2.4 The local average operator M; 3 Unfolding and gradients; 4 Periodic unfolding and the standard homogenization problem; 4.1 The model problem and the standard homogenization result; 4.2 The Unfolding result: the case of strong convergence of the right-hand side; 4.3 Proof of Theorem 4.3; 4.4 The convergence of the energy and its consequences; 4.5 Some corrector results and error estimates; 4.6 The case of weak convergence of the right-hand side; 5 Periodic unfolding and multiscales; 6 Further developments; References 327 $aGabriel Nguetseng and Lazarus Signing Deterministic Homogenization of Stationary Navier-Stokes Type Equations1 Introduction; 2 Periodic homogenization of stationary Navier-Stokes type equations; 2.1 Preliminaries; 2.2 A global homogenization theorem; 2.3 Macroscopic homogenized equations; 3 General deterministic homogenization of stationary Navier-Stokes type equations; 3.1 Preliminaries and statement of the homogenization problem; 3.2 A global homogenization theorem; 3.3 Macroscopic homogenized equations; 3.4 Some concrete examples 327 $a4 Homogenization of the stationary Navier- Stokes equations in periodic porous media4.1 Preliminaries; 4.2 Homogenization results; References; Patricia Donato Homogenization of a Class of Imperfect Transmission Problems; 1 Introduction; 2 Setting of the problem and main results; 3 Some preliminary results; 4 A priori estimates; 5 A class of suitable test functions; 5.1 The test functions in the reference cell Y; 5.2 The test functions in; 6 Proofs of Theorems 2.1 and 2.2; 6.1 Identification of 1 + 2; 6.2 Identification of 1 and 2 for -1 < < 1; 6.3 Identification of u2 327 $a7 Proof of Theorem 2.4 (case > 1)7.1 A priori estimates; 7.2 Identification of 1; 7.3 Identification of 2; References; Georges Griso Decompositions of Displacements of Thin Structures; 1 Introduction; 2 The main theorem; 2.1 Poincar ?e-Wirtinger's inequality in an open bounded set star-shaped with respect to a ball; 2.2 Distances between a displacement and the space of the rigid body displacements; 3 Decomposition of curved rod displacements; 3.1 Notations; 3.2 Elementary displacements and decomposition; 4 Decomposition of shell displacements; 4.1 Notations and preliminary 327 $a4.2 Elementary displacements and decompositions 330 $aThe focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier-Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) 410 0$aSeries in contemporary applied mathematics ;$v16. 606 $aHomogenization (Differential equations)$vCongresses 606 $aDifferential equations, Nonlinear$vCongresses 606 $aMathematical analysis$vCongresses 608 $aElectronic books. 615 0$aHomogenization (Differential equations) 615 0$aDifferential equations, Nonlinear 615 0$aMathematical analysis 676 $a515.353 676 $a518.5 701 $aDamlamian$b Alain$0768005 701 $aMiara$b Bernadette$0891159 701 $aLi$b Daqian$0755910 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910457497603321 996 $aMultiscale problems$92444243 997 $aUNINA