rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations
  name:
    name part: Frénod, Emmanuel.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XI, 126 p. 18 illus., 9 illus. in color. online resource.
  abstract: 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.
  table of contents: I Two-Scale Convergence.- 1 Introduction.- 1.1 First Statements on Two-Scale Convergence.- 1.2 Two-Scale Convergence and Homogenization.- 1.2.1 How Homogenization Led to the Concept of Two-Scale Convergence.- 1.2.2 A Remark Concerning Periodicity.- 1.2.3 A Remark Concerning Weak-* Convergence.- 2 Two-Scale Convergence - Definition and Results.- 2.1 Background Material on Two-Scale Convergence.- 2.1.1 Definitions.- 2.1.2 Link with Weak Convergence.- 2.2 Two-Scale Convergence Criteria.- 2.2.1 Injection Lemma.- 2.2.2 Two-Scale Convergence Criterion.- 2.2.3 Strong Two-Scale Convergence Criterion.- 3 Applications.- 3.1 Homogenization of ODE.- 3.1.1 Textbook Case, Setting and Asymptotic Expansion.- 3.1.2 Justification of Asymptotic Expansion Using Two-Scale Convergence.- 3.2 Homogenization of Singularly-Perturbed ODE.- 3.2.1 Equation of Interest and Setting.- 3.2.2 Asymptotic Expansion Results.- 3.2.3 Asymptotic Expansion Calculations.- 3.2.4 Justification Using Two-Scale Convergence I: Results.- 3.2.5 Justification Using Two-Scale Convergence II: Proofs.- 3.3 Homogenization of Hyperbolic PDE.- 3.3.1 Textbook Case and Setting.- 3.3.2 Order-0 Homogenization.- 3.3.3 Order-1 Homogenization.- 3.4 Homogenization of Singularly-Perturbed Hyperbolic PDE -- 3.4.1 Equation of Interest and Setting -- 3.4.2 An a Priori Estimate -- 3.4.3 Weak Formulation with Oscillating Test Functions -- 3.4.4 Order-0 Homogenization - Constraint -- 3.4.5 Order-0 Homogenization - Equation for V -- 3.4.6 Order-1 Homogenization - Preparations: Equations for U and u -- 3.4.7 Order-1 Homogenization - Strong Two-Scale Convergence of u" -- 3.4.8 Order-1 Homogenization - The Function W1 -- 3.4.9 Order-1 Homogenization - A Priori Estimate and Convergence -- 3.4.10 Order-1 Homogenization - Constraint -- 3.4.11 Order-1 Homogenization - Equation for V1 -- 3.4.12 Concerning Numerics.- II Two-Scale Numerical Methods -- 4 Introduction -- 5 Two-Scale Method for Object Drift with Tide -- 5.1 Motivation and Model -- 5…
  note: by Emmanuel Frénod.
  subject:
    topic: Mathematics
  subject:
    topic: Numerical analysis
  subject:
    topic: Mathematics
  subject:
    topic: Numerical Analysis
  classification: QA297-299.4
  classification: 518
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2190
  identifier: 9783319646688
  identifier: http://dx.doi.org/10.1007/978-3-319-64668-8
  record info:
    record creation date: 171005
    record change date: 20171005165952.0
    record identifier: 978-3-319-64668-8