Multiscale problems [[electronic resource] ] : theory, numerical approximation and applications / / editors, Alain Damlamian, Bernadette Miara, Tatsien Li

• Record Nr.: UNINA9910779068003321
• Pubbl/distr/stampa: Beijing, China, : Higher Education Press, 2011
• ISBN: 981-4366-89-7
• Descrizione fisica: 1 online resource (314 p.)
• Collana: Series in contemporary applied mathematics ; ; 16
• Classificazione: SK 950
• Altri autori (Persone): DamlamianAlain; MiaraBernadette; LiDaqian
• Disciplina: 515.353; 518.5
• Soggetti: Homogenization (Differential equations); Differential equations, Nonlinear; Mathematical analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Preface; 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; 2.3 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; Gabriel 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; 4 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; 7 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; 4.2 Elementary displacements and decompositions
• Sommario/riassunto: The 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)