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  • Textbook
  • © 1994

The Mathematical Theory of Dilute Gases

Part of the book series: Applied Mathematical Sciences (AMS, volume 106)

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  • ISBN: 978-1-4419-8524-8
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Table of contents (13 chapters)

  1. Front Matter

    Pages i-vii
  2. Introduction

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 1-3
  3. Historical Introduction

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 4-12
  4. Informal Derivation of the Boltzmann Equation

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 13-32
  5. Elementary Properties of the Solutions

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 33-62
  6. Rigorous Validity of the Boltzmann Equation

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 63-132
  7. Existence and Uniqueness Results

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 133-166
  8. The Initial Value Problem for the Homogeneous Boltzmann Equation

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 167-190
  9. Perturbations of Equilibria and Space Homogeneous Solutions

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 191-225
  10. Boundary Conditions

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 226-243
  11. Existence Results for Initial-Boundary and Boundary Value Problems

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 244-285
  12. Particle Simulation of the Boltzmann Equation

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 286-311
  13. Hydrodynamical Limits

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 312-335
  14. Open Problems and New Directions

    • Carlo Cercignani, Reinhard Illner, Mario Pulvirenti
    Pages 336-341
  15. Back Matter

    Pages 342-349

About this book

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.

Keywords

  • Boltzmann equation
  • development
  • kinetic theory
  • simulation

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

Authors and Affiliations

  • Dip. di Matematica, Politecnico di Milano, Milano, Italy

    Carlo Cercignani

  • Dept. of Mathematics, University of Victoria, Victoria, Canada

    Reinhard Illner

  • Dip. di Matematica, University of Roma, Roma, Italy

    Mario Pulvirenti

Bibliographic Information

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-8524-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.99
Price excludes VAT (USA)
Hardcover Book USD 139.99
Price excludes VAT (USA)