Appendix Fundamental Properties of Generalized Functions

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Waves and structures in nonlinear nondis 作者：S.N. Gurbatov, O.V. Rudenko,　　 ISBN：978-7-04-031695-7　出版时间：2011-08-30

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Front Matter

Part I Foundations of the Theory of Waves in Nondispersive Media

1 Nonlinear Equations of the First Order

2 Generalized Solutions of Nonlinear Equations

3 Nonlinear Equations of the Second Order

4 Field EvolutionWithin the Framework of the Burgers Equation

5 Evolution of a Noise Field Within the Framework of the Burgers Equation

6 Multidimensional Nonlinear Equations

Part II Mathematical Models and Physical Phenomena in Nonlinear Acoustics

7 Model Equations and Methods of Finding Their Exact Solutions

8 Types of Acoustic Nonlinearities and Methods of Nonlinear Acoustic Diagnostics

9 Nonlinear Sawtooth Waves

10 Self-action of Spatially BoundedWaves Containing Shock Fronts

11 Nonlinear Standing Waves, Resonance Phenomena and Frequency Characteristics of Distributed Systems

Appendix Fundamental Properties of Generalized Functions

Index
- A.1 Definition of generalized functions
- A.2 Fundamental sequences
- A.3 Derivatives of generalized functions
- A.4 The Leibniz formula
- A.5 Derivatives of discontinuous functions
- A.6 Generalized functions of a composite argument
- A.7 Multidimensional generalized functions
- A.8 Continuity equation
- A.8.1 Singular solution
- A.8.2 Green’s function
- A.8.3 Lagrangian and Eulerian coordinates
- A.9 Method of characteristics

Appendix Fundamental Properties of Generalized Functions

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