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Tartar, Luc

From Hyperbolic Systems to Kinetic Theory

Tartar, Luc - From Hyperbolic Systems to Kinetic Theory, e-bok

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ISBN: 9783540775621
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Table of contents

1. Historical Perspective

2. Hyperbolic Systems: Riemann Invariants, Rarefaction Waves

3. Hyperbolic Systems: Contact Discontinuities, Shocks

4. The Burgers Equation and the 1-D Scalar Case

5. The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik

6. Hopf's Formulation of the E-Condition of Oleinik

7. The Burgers Equation: Special Solutions

8. The Burgers Equation: Small Perturbations; the Heat Equation

9. Fourier Transform; the Asymptotic Behaviour for the Heat Equation

10. Radon Measures; the Law of Large Numbers

11. A 1-D Model with Characteristic Speed 1/e

12. A 2-D Generalization; the Perron–Frobenius Theory

13. A General Finite-Dimensional Model with Characteristic Speed 1/e

14. Discrete Velocity Models

15. The Mimura–Nishida and the Crandall–Tartar Existence Theorems

16. Systems Satisfying My Condition (S)

17. Asymptotic Estimates for the Broadwell and the Carleman Models

18. Oscillating Solutions; the 2-D Broadwell Model

19. Oscillating Solutions: the Carleman Model

20. The Carleman Model: Asymptotic Behaviour

21. Oscillating Solutions: the Broadwell Model

22. Generalized Invariant Regions; the Varadhan Estimate

23. Questioning Physics; from Classical Particles to Balance Laws

24. Balance Laws; What Are Forces?

25. D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation

26. Cauchy: from Masslets and Springs to 2-D Linearized Elasticity

27. The Two-Body Problem

28. The Boltzmann Equation

29. The Illner–Shinbrot and the Hamdache Existence Theorems

30. The Hilbert Expansion

31. Compactness by Integration

32. Wave Front Sets; H-Measures

33. H-Measures and “Idealized Particles”

34. Variants of H-Measures

35. Biographical Information

36. Abbreviations and Mathematical Notation

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Nyckelord: MATHEMATICS / General MAT000000

Författare
Utgivare
Springer
Utgivningsår
2008
Språk
en
Utgåva
1
Kategori
Naturvetenskaper
Format
E-bok
eISBN (PDF)
9783540775621

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