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This volume is intended to coverthe presentstatus of the mathematicaltools used to deal with problems related to slow rare?ed ?ows. The meaning and usefulness of the subject, and the extent to which it is covered in the book, are discussed in some detail in the introduction. In short, I tried to present the basic concepts and the techniques used in probing mathematical questions and problems which arise when studying slow rare?ed ?ows in environmental sciences and micromachines. For the book to be up-to-date without being excessively large, it was necessary to omit some topics, which are treated elsewhere, as indicated in the introd- tion and, whenever the need arises, in the various chapters of this volume. 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. Although I have tried to give a rather complete bibliographical coverage,the choice of the topics and of the references certainly re?ects a personal bias and I apologize in advance for any omission. I wish to thank Lorenzo Valdettaro, Antonella Abb` a, Silva Lorenzani and Paolo Barbante for their help with pictures and especially Professor Ching Shen for his permission to reproduce his pictures on microchannel ?ows.
List of contents
The Boltzmann Equation.- Validity and Existence.- Perturbations of Equilibria.- Boundary Value Problems.- Slow Flows in a Slab.- Flows in More Than One Dimension.- Rarefied Lubrication in Mems.
Summary
This volume is intended to coverthe presentstatus of the mathematicaltools used to deal with problems related to slow rare?ed ?ows. The meaning and usefulness of the subject, and the extent to which it is covered in the book, are discussed in some detail in the introduction. In short, I tried to present the basic concepts and the techniques used in probing mathematical questions and problems which arise when studying slow rare?ed ?ows in environmental sciences and micromachines. For the book to be up-to-date without being excessively large, it was necessary to omit some topics, which are treated elsewhere, as indicated in the introd- tion and, whenever the need arises, in the various chapters of this volume. 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. Although I have tried to give a rather complete bibliographical coverage,the choice of the topics and of the references certainly re?ects a personal bias and I apologize in advance for any omission. I wish to thank Lorenzo Valdettaro, Antonella Abb` a, Silva Lorenzani and Paolo Barbante for their help with pictures and especially Professor Ching Shen for his permission to reproduce his pictures on microchannel ?ows.
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From the reviews:
“The main topic of the book is rarefied gas dynamics which can be defined as the study of gas flows in which the distance between two subsequent collisions of a molecule … is not negligible in comparison with the length typical for the surrounding structure. … The book will be useful to specialists in the mathematical theory of fluids. It can serve also those who are beginners in this area provided they have some erudition in mathematics on graduate level.” (Ivan Straškraba, Applications of Mathematics, Vol. 54 (4), 2009)
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From the reviews: "The main topic of the book is rarefied gas dynamics which can be defined as the study of gas flows in which the distance between two subsequent collisions of a molecule ... is not negligible in comparison with the length typical for the surrounding structure. ... The book will be useful to specialists in the mathematical theory of fluids. It can serve also those who are beginners in this area provided they have some erudition in mathematics on graduate level." (Ivan Straskraba, Applications of Mathematics, Vol. 54 (4), 2009)
