edited by N Bellomo (Politecnico di Torino, Italia)

This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.

• On the Cauchy Problem for the Boltzmann Equation (L Arlotti & N Bellomo)
• Asymptotic Analysis of Nonlinear Kinetic Equations: The Hydrodynamic Limit (M Lachowicz)
• An Introduction to Kinetic Theory of Dense Gases (J Polewczak)
• Computational Methods for the Boltzmann Equation (W Walu()
• General Bibliography