Waves in Continuous Media

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.

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

Auteur
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

Contenu

1. Hyperbolic waves.- 2. Dispersive waves.- 3. Water waves.