Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations
Authors: Frénod, Emmanuel
Free Preview- Provides a very affordable approach to the homogenization theory
- Gives a complete vision - from theory to numerics - of consequences of strong oscillations in transport phenomena Contains several applications from environment questions to Iter plasmas
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- About this book
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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.
- About the authors
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Emmanuel Frénod is Professor of Applied Mathematics at Université Bretagne Sud.
- Reviews
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“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)
- Table of contents (6 chapters)
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Introduction
Pages 3-19
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Two-Scale Convergence: Definition and Results
Pages 21-33
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Applications
Pages 35-87
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Introduction
Pages 91-91
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Two-Scale Numerical Method for the Long-Term Forecast of the Drift of Objects in an Ocean with Tide and Wind
Pages 93-107
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations
- Authors
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- Emmanuel Frénod
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 2190
- Copyright
- 2017
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-64668-8
- DOI
- 10.1007/978-3-319-64668-8
- Softcover ISBN
- 978-3-319-64667-1
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- XI, 126
- Number of Illustrations
- 9 b/w illustrations, 9 illustrations in colour
- Topics
