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© 2017

Waves in Continuous Media

Benefits

  • This book aims to promote a problem solving approach to teaching the wave propagation in continuous media

  • This book contains more than 200 problems covering mostly compressible fluid mechanics and surface wave propagation in incompressible (homogeneous or non) fluids

  • Answers each problem considered as a new material to deeper understanding qualitative and quantitative properties of wave models rather than a simple application of the methods presented

Book

Table of contents

  1. Front Matter
    Pages i-viii
  2. S. L. Gavrilyuk, N. I. Makarenko, S. V. Sukhinin
    Pages 1-41
  3. S. L. Gavrilyuk, N. I. Makarenko, S. V. Sukhinin
    Pages 43-76
  4. S. L. Gavrilyuk, N. I. Makarenko, S. V. Sukhinin
    Pages 77-136
  5. Back Matter
    Pages 137-141

About this book

Introduction

Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and  conservation laws for  quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations.

Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids.

The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations.

Keywords

hyperbolic waves dispersive waves surface internal waves waves

Authors and affiliations

  1. 1.Aix-Marseille UniversityMarseilleFrance
  2. 2.Russian Academy of Sciences Lavrentyev Institute of HydrodynamicsNovosibirsk State UniversityNovosibirskRussia
  3. 3.Russian Academy of Sciences Lavrentyev Institute of HydrodynamicsNovosibirsk State UniversityNovosibirskRussia

About the authors

Sergey Gavrilyuk is professor at the Aix-Marseille III University, Marseille, France

Nikolai MAKARENKO is professor at the Lavrentyev Institute of Hydrodynamics Siberian Branch of the Russian Academy, Novosibirsk, Russia

Sergey SUKHININ is professor at the Lavrentyev Institute of Hydrodynamics Russian Academy of Sciences, Novosibirsk, Russia

Bibliographic information

  • Book Title Waves in Continuous Media
  • Authors S. L. Gavrilyuk
    N.I. Makarenko
    S.V. Sukhinin
  • Series Title Lecture Notes in Geosystems Mathematics and Computing
  • Series Abbreviated Title Lecture Notes in Geosystems Mathematics and Computing
  • DOI https://doi.org/10.1007/978-3-319-49277-3
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-49276-6
  • eBook ISBN 978-3-319-49277-3
  • Edition Number 1
  • Number of Pages VIII, 141
  • Number of Illustrations 15 b/w illustrations, 0 illustrations in colour
  • Topics Partial Differential Equations
  • Buy this book on publisher's site
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Reviews

“This book is a graduate level text based upon a lecture course on waves in continuous media with particular emphasis on fluid media. It is aimed at students of applied mathematics, mechanics and geophysics. … Waves in a stratified fluid and stability of such waves are also discussed. A number of instructive examples and exercises are given that may be useful for the targeted audience.” (Fiazud Din Zaman, zbMATH 1364.76003, 2017)