Shock waves

Shock waves

by Liu, Tai-Ping

Type Book
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This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws.The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to…

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Title Statements

  • Full title :Shock waves / Tai-Ping Liu.

Summary

This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws.The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws. This is a most significant well-posedness theory for.

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Edition Statements

  • Publication Date:2021

Publication Statements

The Physical Object

  • Description:1 online resource (xvii, 437 pages) : : illustrations.

Edition Identifiers

  • ISBN:9781470466244, 1470466244
  • oclc:on1273969407
  • LC Classification:QA930
  • Dewey Decimal:515/.3535

Table of Contents

Intro -- Preface -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 1. Method of Characteristics -- 2. Development of Singularities -- 3. Weak Solutions, Rankine-Hugoniot Condition -- 4. Expansion Waves -- 5. Non-uniqueness, Entropy Condition -- 6. Notes -- 7. Exercises -- Chapter 3. Scalar Convex Conservation Laws -- 1. Riemann Problem -- 2. Hopf Equation -- 3. Wave Interactions, Constructing Solutions -- 4. Well-Posedness Theory -- 5. Generalized Characteristics, Nonlinear Regularization -- 6. -Waves, Inviscid Dissipation -- 7. Entropy Pairs -- 8. Generalized Entropy Functional

9. Notes -- 10. Exercises -- Chapter 4. Burgers Equation -- 1. Heat Equation -- 2. Hopf-Cole Transformation -- 3. Inviscid Limit -- 4. Nonlinear Waves -- 5. Linearized Hopf-Cole Transformation -- 6. Green's Functions -- 7. Nonlinearity -- 8. Metastable States -- 9. Notes -- 10. Exercises -- Chapter 5. General Scalar Conservation Laws -- 1. Viscous Shock Profiles -- 2. Riemann Problem -- 3. ₁ Stability -- 4. Scattering Wave Patterns -- 5. Entropy Pairs -- 6. Multi-Dimensional Laws -- 7. Notes -- 8. Exercises -- Chapter 6. Systems of Hyperbolic Conservation Laws: General Theory -- 1. Hyperbolicity

…

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Subjects

Ondes de choc -- Modèles mathématiques Shock waves -- Mathematical models

Writers

Liu, Tai-Ping

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