Waves in Continuous Media
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Beschreibung
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.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
Autor*in
S. L. Gavrilyuk
Themen in »Waves in Continuous Media«
hyperbolic waves dispersive waves surface internal waves waves partial differential equations
Stimmen zu »Waves in Continuous Media«
“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)
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