Sharma Quasilinear Hyperbolic Systems, Compressible Flows, and Waves

1. Auflage 2010
ISBN: 978-1-4398-3691-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 282 Seiten

Reihe: Monographs and Surveys in Pure and Applied Mathematics

Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field.

After linking continuum mechanics and quasilinear partial differential equations, the book discusses the scalar conservation laws and hyperbolic systems in two independent variables. Using the method of characteristics and singular surface theory, the author then presents the evolutionary behavior of weak and mild discontinuities in a quasilinear hyperbolic system. He also explains how to apply weakly nonlinear geometrical optics in nonequilibrium and stratified gas flows and demonstrates the power, generality, and elegance of group theoretic methods for solving Euler equations of gasdynamics involving shocks. The final chapter deals with the kinematics of a shock of arbitrary strength in three dimensions.

With a focus on physical applications, this text takes readers on a journey through this fascinating area of applied mathematics. It provides the essential mathematical concepts and techniques to understand the phenomena from a theoretical standpoint and to solve a variety of physical problems.

Zielgruppe

Graduate students and researchers in applied mathematics, physics, and engineering interested in fluid dynamics, gas dynamics, and mechanics.

Autoren/Hrsg.

Sharma, Vishnu D.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Algebra
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Naturwissenschaften Physik Physik Allgemein

Inhaltsverzeichnis

Hyperbolic Systems of Conservation Laws
Preliminaries
Examples

Scalar Hyperbolic Equations in One Dimension
Breakdown of Smooth Solutions
Entropy Conditions Revisited
Riemann Problem for Nonconvex Flux Function
Irreversibility
Asymptotic Behavior

Hyperbolic Systems in One Space Dimension
Genuine Nonlinearity
Weak Solutions and Jump Condition
Entropy Conditions
Riemann Problem
Shallow Water Equations

Evolution of Weak Waves in Hyperbolic Systems
Waves and Compatibility Conditions
Evolutionary Behavior of Acceleration Waves
Interaction of Shock Waves with Weak Discontinuities
Weak Discontinuities in Radiative Gasdynamics
One-Dimensional Weak Discontinuity Waves
Weak Nonlinear Waves in an Ideal Plasma
Relatively Undistorted Waves

Asymptotic Waves for Quasilinear Systems
Weakly Nonlinear Geometrical Optics
Far Field Behavior
Energy Dissipated across Shocks
Evolution Equation Describing Mixed Nonlinearity
Singular Ray Expansions
Resonantly Interacting Waves

Self-Similar Solutions Involving Discontinuities and Their Interaction
Waves in Self-Similar Flows
Imploding Shocks in a Relaxing Gas
Exact Solutions of Euler Equations via Lie Group Analysis

Kinematics of a Shock of Arbitrary Strength
Shock Wave through an Ideal Gas in 3-Space Dimensions
An Alternative Approach Using the Theory of Distributions
Kinematics of a Bore over a Sloping Beach

Bibliography
Index

Über Autor(innen)

Vishnu D. Sharma is chair professor in the Department of Mathematics at the Indian Institute of Technology, Bombay (IITB). Dr. Sharma is also president of the Indian Society of Theoretical and Applied Mechanics.