Mathematical Topics In Nonlinear Kinetic Theory

Contents:

*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