Mathematical Topics in Nonlinear Kinetic Theory

This book has the aim of dealing with the Nonlinear evolution problems related to the spatially dependent Boltzmann and Enskog equations.

• Nonlinear Boltzmann Equation:
  • The Distribution Function, The Nonlinear Boltzmann Equation, Elementary Properties of the Boltzmann Equation, Plan of the Book
• The Cauchy Problem for Initial Data Decaying at Infinity:
  • Nonlinear Boltzmann-Type Equations
  • Existence and Uniqueness, Fundamental Inequalities and Main Results, Physical Consistency of the Results, H-Theorem and Asymptotic Behaviour of the Solution, Existence Theory near a Local Maxwellian, The Iteration Scheme in Presence of Boundaries
• The Cauchy Problem for Initial Data Close to Equilibrium:
  • Local Existence Theorem, Global Existence in a Bounded Domain, Global Existence in R³, Other Global Existence Results
• Kinetic Equations for Dense Gases:
  • The Enskog Equation, The Initial Value Problem for the Enskog Equation, Asymptotic Equivalence Between the Boltzmann and Enskog Equations
• Open Problems and Exercises:
  • On the Initial Value Problem, The Initial-Boundary Value Problem, The Semidiscrete Boltzmann Equation
• The Linearized Boltzmann Equation:
  • Basic Properties of the Linearized Boltzmann Operator, The Linearized Boltzmann Operator in a Bounded Rectangular Domain, The Resolvent of the Boltzmann Operator, The Spectrum of the Boltzmann Operator in a Bounded Domain, The Boltzmann Semigroup in a Bounded Domain, The Boltzmann Semigroup in R³