Hyperbolic Conservation Laws in Continuum Physics

  • Constantine M. Dafermos

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 325)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Constantine M. Dafermos
    Pages 1-18
  3. Constantine M. Dafermos
    Pages 19-35
  4. Constantine M. Dafermos
    Pages 37-47
  5. Constantine M. Dafermos
    Pages 49-60
  6. Constantine M. Dafermos
    Pages 61-82
  7. Constantine M. Dafermos
    Pages 83-119
  8. Constantine M. Dafermos
    Pages 121-145
  9. Constantine M. Dafermos
    Pages 147-174
  10. Constantine M. Dafermos
    Pages 175-202
  11. Constantine M. Dafermos
    Pages 203-208
  12. Constantine M. Dafermos
    Pages 209-237
  13. Constantine M. Dafermos
    Pages 239-297
  14. Constantine M. Dafermos
    Pages 299-335
  15. Constantine M. Dafermos
    Pages 337-369
  16. Constantine M. Dafermos
    Pages 371-395
  17. Back Matter
    Pages 397-446

About this book

Introduction

The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler; by the mid-nineteenth century, the trees were fully grown and ready to yield fruit. It was in this envi­ ronment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conserva­ tion laws"; and these two subjects have been traveling hand-in-hand over the past one hundred and fifty years. This book aims at presenting the theory of hyper­ bolic conservation laws from the standpoint of its genetic relation to Continuum Physics. Even though research is still marching at a brisk pace, both fields have attained by now the degree of maturity that would warrant the writing of such an exposition. In the realm of Continuum Physics, material bodies are realized as continuous media, and so-called "extensive quantities", such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws and constitutive equations. A self-contained, though skeletal, introduction to this branch of classical physics is presented in Chapter II. The reader may flesh it out with the help of a specialized text on the subject.

Keywords

Boundary value problem Entropy hyperbolic conservation laws partial differential equation partial differential equations thermodynamics

Authors and affiliations

  • Constantine M. Dafermos
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-22019-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-22021-4
  • Online ISBN 978-3-662-22019-1
  • Series Print ISSN 0072-7830
  • About this book