January  2009, 24(1): i-ii. doi: 10.3934/dcds.2009.24.1i

Preface

1. 

Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Trieste 63, 35121 - Padova

2. 

S.I.S.S.A. (I.S.A.S.), Via Beirut 2/4, 34013 Trieste

3. 

Penn State University Mathematics Dept., University Park, State College, PA 16802

Published  January 2009

The famous Boltzmann equation

$frac{\partial f}{\partial t} + v \cdot \nabla_x f = Q(f,f),$

studied in a classic paper of Ludwig Boltzmann (1872), represents the basic example of a kinetic equation. It describes the evolution of a distribution of particles subject to binary collisions. Since then, the field has become extremely vast and active, and in recent years two of the main problems concerning this equation have been solved: the Cauchy problem for quite general collision kernels and the convergence towards Navier-Stokes and Euler equation under suitable rescalings.
Ludwig E. Boltzmann ended his life in Duino, near Trieste, on September 5, 1906. The conference

Boltzmann equations and applications, SISSA, Trieste, June 12-17, 2006

was organized with the double aim of honoring this great mathematician and reviewing the most recent and exciting developments on kinetic equations. Two main courses, given by L. Saint-Raymond and C. Villani, and a series of lectures held by leading mathematicians working in this area, allowed participants from all over the world to become acquainted with the most interesting results and research directions.

For more information please click the "Full Text" above.

Citation: Fabio Ancona, Stefano Bianchini, Alberto Bressan. Preface. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : i-ii. doi: 10.3934/dcds.2009.24.1i
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