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Nonlinear Hyperbolic Waves in Multidimensions

Nonlinear Hyperbolic Waves in Multidimensions by Phoolan Prasad
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AN INTRODUCTION TO NONLINEAR HYPERBOLIC WAVES
A Wave Equation with Genuine Nonlinearity
Breakdown of a Genuine Solution
Conservation Law and Jump Condition
Stability Consideration, Entropy Condition, and Shocks
Some Examples
Shock Structure, Dissipation and Entropy Condition
The Persistence of a Shock
Nonlinear Wavefront and Shock Front
Hopf's Result on the General Solution
Equal Area Rule for Shock Fitting
HYPERBOLIC SYSTEM-SOME BASIC RESULTS
Hyperbolic System of First Order Equations in Two Independent Variables
The Wave Equation in m(>1) Space Dimensions
Hyperbolic System in More than Two Independent Variables
Bicharacteristic Curves, Rays, and Compatibility Condition
Propagation of Discontinuities of First Order Derivatives Along Rays
SIMPLE WAVE, HIGH FREQUENCY APPROXIMATION, AND RAY THEORY
Simple Wave
High-Frequency Approximation, Wavefront, Huygens' Method and Fermat's Principle
Kinematics of a Propagating Curve
Breakdown of the Continuity of a Solution of a Quasilinear System
Jump Conditions for a Curved Shock
WEAKLY NONLINEAR RAY THEORY (WNLRT) DERIVATION
A Historical Account
Derivation of CPW Theory
A Geometric Derivation of WNLRT
An Asymptotic Derivation of WNLRT
STABILITY OF SOLUTIONS NEAR A SINGULARITY OF SONIC TYPE
Introduction
One-Dimensional Weakly Nonlinear Wave Propagation
Waves in a Multi-Dimensional Steady Transonic Flow
WNLRT IN A POLYTROPIC GAS
Basic Equations
Geometrical Features of a Nonlinear Wavefront
Exact Solution of an Initial Value Problem
Conclusion and Validity of WNLRT
COMPATIBILITY CONDITIONS ON A SHOCK: SINGLE CONSERVATION LAW
Derivation of the Infinite System of Compatibility Conditions
Existence and Uniqueness of the Solution of the Infinite System
A New Theory of Shock Dynamics: Analytic Considerations
A New Theory of Shock Dynamics: Comparison of Numerical Results with the Exact Solution
Conclusion
ONE-DIMENSIONAL PISTON PROBLEM: AN APPLICATION OF NTSD
Formulation of the Problem
Dynamical Compatibility Conditions
Initial Conditions for the Piston Problem
Results and Discussions
COMPATIBILITY CONDITIONS ON A MULTI-DIMENSIONAL SHOCK
Shock Rays
Shock Manifold Equation for a Weak Shock
Geometrical and Kinematical Compatibility Conditions
Dynamical Compatibility Conditions
A Weak Shock Ray Theory
PROPAGATION OF A CURVED WEAK SHOCK
Governing Equations of the NTSD
Conservation Form of the Equations for a 2-Dimensional Shock Propagation
Initial Conditions, Results, and Discussion
Comparison with other Theories
Corrugational Stability and Persistence of a Kink
CRC Press; May 2001
355 pages; ISBN 9781420026146
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Title: Nonlinear Hyperbolic Waves in Multidimensions
Author: Phoolan Prasad
 
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