Two-scale approach to oscillatory singularly perturbed transport equations / Emmanuel Frénod

Auteur: Frénod, Emmanuel (1968-) - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 2190Langue: anglaisPays: SwisseÉditeur: Cham : Springer, 2017Description: 1 vol. (XI-124 p.) : fig. en coul. ; 24 cm ISBN: 9783319646671 ; br. ISSN: 0075-8434Résumé: Publisher's description: "This book presents the classical results of the two-scale convergence theory and explains—using several figures—why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master's and PhD students interested in homogenization and numerics, as well as to the Iter community.''.Bibliographie: Bibliogr. p. 121-124. Sujets MSC: 65L11 Numerical analysis -- Ordinary differential equations -- Singularly perturbed problems
65-02 Numerical analysis -- Research exposition (monographs, survey articles)
34D15 Ordinary differential equations -- Stability theory -- Singular perturbations
35B25 Partial differential equations -- Qualitative properties of solutions -- Singular perturbations
35B27 Partial differential equations -- Qualitative properties of solutions -- Homogenization; equations in media with periodic structure
En-ligne: Zentralblatt | MSN
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Bibliogr. p. 121-124

Publisher's description: "This book presents the classical results of the two-scale convergence theory and explains—using several figures—why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master's and PhD students interested in homogenization and numerics, as well as to the Iter community.''

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