Tartar, Luc
From Hyperbolic Systems to Kinetic Theory
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
DRM-restrictions
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Keywords: MATHEMATICS / General MAT000000
- Author(s)
- Tartar, Luc
- Publisher
- Springer
- Publication year
- 2008
- Language
- en
- Edition
- 1
- Category
- Natural Sciences
- Format
- Ebook
- eISBN (PDF)
- 9783540775621