Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations

Beschreibung

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.
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

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

Autor*in

Emmanuel Frénod

Themen in »Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations«

Homogenization Singular perturbation Oscillations Transport phenomena Plasma

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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)
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