From Hyperbolic Systems to Kinetic Theory A Personalized Quest
Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical re...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2008, 2008
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| Edition: | 1st ed. 2008 |
| Series: | Lecture Notes of the Unione Matematica Italiana
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| Subjects: | |
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| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Historical Perspective
- Hyperbolic Systems: Riemann Invariants, Rarefaction Waves
- Hyperbolic Systems: Contact Discontinuities, Shocks
- The Burgers Equation and the 1-D Scalar Case
- The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik
- Hopf's Formulation of the E-Condition of Oleinik
- The Burgers Equation: Special Solutions
- The Burgers Equation: Small Perturbations; the Heat Equation
- Fourier Transform; the Asymptotic Behaviour for the Heat Equation
- Radon Measures; the Law of Large Numbers
- A 1-D Model with Characteristic Speed 1/?
- A 2-D Generalization; the Perron–Frobenius Theory
- A General Finite-Dimensional Model with Characteristic Speed 1/?
- Discrete Velocity Models
- The Mimura–Nishida and the Crandall–Tartar Existence Theorems
- Systems Satisfying My Condition (S)
- Asymptotic Estimates for the Broadwell and the Carleman Models
- Oscillating Solutions; the 2-D Broadwell Model
- Oscillating Solutions: the Carleman Model
- The Carleman Model: Asymptotic Behaviour
- Oscillating Solutions: the Broadwell Model
- Generalized Invariant Regions; the Varadhan Estimate
- Questioning Physics; from Classical Particles to Balance Laws
- Balance Laws; What Are Forces?
- D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation
- Cauchy: from Masslets and Springs to 2-D Linearized Elasticity
- The Two-Body Problem
- The Boltzmann Equation
- The Illner–Shinbrot and the Hamdache Existence Theorems
- The Hilbert Expansion
- Compactness by Integration
- Wave Front Sets; H-Measures
- H-Measures and “Idealized Particles”
- Variants of H-Measures
- Biographical Information
- Abbreviations and Mathematical Notation