Shock waves
著者
書誌事項
Shock waves
（Graduate studies in mathematics, 215）（Applied mathematics）
American Mathematical Society, c2021
- : hardcover
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注記
Includes bibliographical references (p. 427-433) and index
内容説明・目次
内容説明
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 weak solutions of quasilinear evolutionary partial differential equations. The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models. Potentially interesting questions and research directions are also raised in these chapters.
The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering, and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.
目次
Introduction
Preliminaries
Scalar convex conservation laws
Burgers equation
General scalar conservation laws
System of hyperbolic conservation laws, general theory
Riemann problem
Wave interactions
Well-posedness theory
Viscosity
Relaxation
Nonlinear resonance
Multi-dimensional gas flows
Concluding remarks
Bibliography
Index
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