Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations

1. Front Matter

   Pages i-xi

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2. Two-Scale Convergence

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Emmanuel Frénod

      Pages 3-19

   3. Two-Scale Convergence: Definition and Results

      • Emmanuel Frénod

      Pages 21-33

   4. Applications

      • Emmanuel Frénod

      Pages 35-87

3. Two-Scale Numerical Methods

   1. Front Matter

      Pages 89-89

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   2. Introduction

      • Emmanuel Frénod

      Pages 91-91

   3. Two-Scale Numerical Method for the Long-Term Forecast of the Drift of Objects in an Ocean with Tide and Wind

      • Emmanuel Frénod

      Pages 93-107

   4. Two-Scale Numerical Method for the Simulation of Particle Beams in a Focussing Channel

      • Emmanuel Frénod

      Pages 109-119

4. Back Matter

   Pages 121-126

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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.




 

• Homogenization
• Singular perturbation
• Oscillations
• Transport phenomena
• Plasma

“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)

• LMBA, Université Bretagne Sud, Vannes, France

  Emmanuel Frénod

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

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