Mathematical Topics in Nonlinear Kinetic Theory II

The following sections are included:

• ACKNOWLEDGMENTS

• PREFACE

• CONTENTS

The following sections are included:

• The One Particle Distribution Function and the Boltzmann Equation

• The Standard Enskog Equation
  • Method 1
  • Method 2

• The Revised Enskog Equation

• Classification of Enskog Type Models

• On Mathematical Formulation of Problems

• Plan of the Book

• References

The following sections are included:

• Introduction

• Existence and Uniqueness: Basic Notations

• Existence and Uniqueness of Mild Solutions

• Existence and Uniqueness of Classical Solutions

• Asymptotic Behaviour in Time

• On the H-Theorem for the Abstract (Revised) Enskog Equation

• References

The following sections are included:

• Introduction

• Basic a Priori Estimations

• Formulation of Existence Theorems

• Convergence and Stability Results

• Existence and Some Properties of Approximate Solutions

• References

The following sections are included:

• Introduction

• Asymptotic Equivalence between the Abstract Enskog Equation and the Boltzmann Equation for Decaying Data

• Asymptotic Equivalence Between the Abstract Enskog and the Boltzmann Equation in L₁

• Some Open Problems
  • Asymptotic Behaviour of Solutions of the Abstract Enskog Equation for Small Knudsen Numbers
  • Asymptotic Equivalence between the Abstract Enskog Equation and the Boltzmann Equation in the Presence of an External Force Field

• References

The following sections are included:

• Introduction

• On the Initial–Boundary Value Problem

• On the Initial Value Problem
  • On the Initial Value Problem for Decaying Data
  • Uniqueness in the Initial Value Problem with Large L₁ Initial Conditions
  • Analysis of Some Aspects of Fluid-Dynamic Flows

• On the Mathematical Modelling

• On the Semidiscrete Enskog Equation

• References

The following sections are included:

• AUTHOR INDEX