Bücher von Carlo Cercignani

This volume contains the text of four sets of lecturesdelivered at the third session of the Summer Schoolorganized by C.I.M.E. (Centro Internazionale MatematicoEstivo). These texts are preceded by an introduction writtenby C. Cercignani and M. Pulvirenti which summarizes thepresent status in the area of Nonequilibrium Problems inMany-Particle Systems and tries to put the contents of thedifferent sets of lectures in the right perspective, inorder to orient the reader. The lectures deal with theglobal existence of weak solutions for kinetic models andrelated topics, the basic concepts of non-standard analysisand their application to gas kinetics, the kinetic equationsfor semiconductors and the entropy methods in the study ofhydrodynamic limits. CONTENTS: C. Cercignani, M. Pulvirenti: NonequilibriumProblems in Many-Particle Systems. An Introduction.- L. Arkeryd: Some Examples of NSA in Kinetic Theory.- P.L. Lions: Global Solutions of Kinetic Models and RelatedProblems.- P.A. Markowich: Kinetic Models forSemiconductors.- S.R.S. Varadhan: Entropy Methods inHydrodynamic Scaling.

Features an exposition of the present status of the theory of the Boltzmann equation and its applications. The Boltzmann equation, an integrodifferential equation established by Boltzmann in 1872 to describe the state of a dilute gas, forms the basis for the kinetic theory of gases.

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity.

This volume is intended to coverthe presentstatus of the mathematicaltools used to deal with problems related to slow rare?ed ?ows. Their omission does not alter the aim of the book, to provide an understanding of the essential mathematical tools required to deal with slow rare?ed ?ows and give the background for a study of the original literature.

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity.

The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers.

Covers scaling limits and modelling in equations of mathematical physics. This book covers basic concepts of the kinetic theory of gases which is not only important in its own right but also as a prototype of a mathematical construct central to the theory of non-equilibrium phenomena in large systems.