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Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations

  • Emmanuel Frénod

Part of the Lecture Notes in Mathematics book series (LNM, volume 2190)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Two-Scale Convergence

    1. Front Matter
      Pages 1-1
    2. Emmanuel Frénod
      Pages 3-19
    3. Emmanuel Frénod
      Pages 21-33
    4. Emmanuel Frénod
      Pages 35-87
  3. Two-Scale Numerical Methods

  4. Back Matter
    Pages 121-126

About this book

Introduction

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.

Keywords

Homogenization Singular perturbation Oscillations Transport phenomena Plasma

Authors and affiliations

  • Emmanuel Frénod
    • 1
  1. 1.LMBAUniversité Bretagne SudVannesFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-64668-8
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-64667-1
  • Online ISBN 978-3-319-64668-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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