From Hyperbolic Systems to Kinetic Theory A Personalized Quest

From Hyperbolic Systems to Kinetic Theory A Personalized Quest / by Luc Tartar.

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Bibliographic Details
Main Author: Tartar, Luc (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008.
Edition:1st ed. 2008.
Series:Lecture Notes of the Unione Matematica Italiana, 6
Springer eBook Collection.
Subjects:
Partial differential equations.
Continuum physics.
Physics.
Dynamics.
Ergodic theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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