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© 2017

Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations

Book
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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

  1. 1.LMBAUniversité Bretagne SudVannesFrance

About the authors

Emmanuel Frénod is Professor of Applied Mathematics at Université Bretagne Sud.

Bibliographic information

  • Book Title Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations
  • Authors Emmanuel Frénod
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • 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 Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-64667-1
  • eBook ISBN 978-3-319-64668-8
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XI, 126
  • Number of Illustrations 9 b/w illustrations, 9 illustrations in colour
  • Topics Numerical Analysis
  • Buy this book on publisher's site
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Reviews

“This is a good research monograph for people working on theoretical and numerical aspects of oscillatory singularly perturbed differential equations. The book is well-written with several examples from various applications. This book provides the complete picture of two-scale convergence approach for homogenization problems and the numerical approach. This monograph is excellent and well-written. This book will be very useful for mathematicians and engineers working on multiscale problems.” (Srinivasan Natesan, zbMATH 1383.65084, 2018)