Applied Mathematical Sciences

The Mathematical Theory of Dilute Gases

Authors: Cercignani, Carlo, Illner, Reinhard, Pulvirenti, Mario

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About this Textbook

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. The project was in some sense inherited from our friend Marvin Shinbrot, who had planned a book about recent progress for the Boltzmann equation, but, due to his untimely death in 1987, never got to do it. When we drew up the first outline, we could not anticipate how long the actual writing would stretch out. Our ambitions were high: We wanted to cover the modern mathematical theory of the Boltzmann equation, with rigorous proofs, in a complete and readable volume. As the years progressed, we withdrew to some degree from this first ambition- there was just too much material, too scattered, sometimes incomplete, sometimes not rigorĀ­ ous enough. However, in the writing process itself, the need for the book became ever more apparent. The last twenty years have seen an amazing number of significant results in the field, many of them published in incomĀ­ plete form, sometimes in obscure places, and sometimes without technical details. We made it our objective to collect these results, classify them, and present them as best we could. The choice of topics remains, of course, subjective.

Reviews

"...this is a volume that will repay close study by those who wish to catch up with the present state of the art in the mathematical theory of dilute gases." - Journal of Fluid Mechanics

Table of contents (13 chapters)

  • Introduction

    Cercignani, Carlo (et al.)

    Pages 1-3

  • Historical Introduction

    Cercignani, Carlo (et al.)

    Pages 4-12

  • Informal Derivation of the Boltzmann Equation

    Cercignani, Carlo (et al.)

    Pages 13-32

  • Elementary Properties of the Solutions

    Cercignani, Carlo (et al.)

    Pages 33-62

  • Rigorous Validity of the Boltzmann Equation

    Cercignani, Carlo (et al.)

    Pages 63-132

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4419-8524-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-0-387-94294-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-1-4612-6425-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Mathematical Theory of Dilute Gases
Authors
Series Title
Applied Mathematical Sciences
Series Volume
106
Copyright
1994
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4419-8524-8
DOI
10.1007/978-1-4419-8524-8
Hardcover ISBN
978-0-387-94294-0
Softcover ISBN
978-1-4612-6425-5
Series ISSN
0066-5452
Edition Number
1
Number of Pages
VII, 349
Topics