Bøger af Mario Pulvirenti

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.

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.

Incompressible flows have been attached, by many distinguished mathe maticians, with a large variety of mathematical techniques so that, today, this field constitutes a very rich and stimulating part of applied mathematics.