Quasilinear Hyperbolic Systems, Compressible Flows, and Waves

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CRC Press, Apr 29, 2010 - Mathematics - 282 pages
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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.

 

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Contents

Hyperbolic Systems of Conservation Laws
1
Scalar Hyperbolic Equations in One Dimension
15
Hyperbolic Systems in One Space Dimension
39
Evolution of Weak Waves in Hyperbolic Systems
75
Asymptotic Waves for Quasilinear Systems
133
SelfSimilar Solutions Involving Discontinuities
165
Kinematics of a Shock of Arbitrary Strength
205
Bibliography
249
Index
265
Back Cover
269
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About the author (2010)

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.

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