Overview
- 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
Part of the book series: Lecture Notes in Geosystems Mathematics and Computing (LNGMC)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.Similar content being viewed by others
Keywords
Table of contents (3 chapters)
-
Front Matter
-
Back Matter
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)
Authors and Affiliations
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
DOI: https://doi.org/10.1007/978-3-319-49277-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-49276-6Published: 03 February 2017
eBook ISBN: 978-3-319-49277-3Published: 27 January 2017
Series ISSN: 2730-5996
Series E-ISSN: 2512-3211
Edition Number: 1
Number of Pages: VIII, 141
Number of Illustrations: 15 b/w illustrations
Topics: Partial Differential Equations