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© 1984

Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables

Book

Part of the Applied Mathematical Sciences book series (AMS, volume 53)

Table of contents

  1. Front Matter
    Pages i-viii
  2. A. Majda
    Pages 1-29
  3. Back Matter
    Pages 157-159

About this book

Introduction

Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con­ strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm.

Keywords

Erhaltungssatz Gasdynamik Kompressible Strömung Stosswelle Systems flow

Authors and affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • Book Title Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
  • Authors A. Majda
  • Series Title Applied Mathematical Sciences
  • DOI https://doi.org/10.1007/978-1-4612-1116-7
  • Copyright Information Springer-Verlag New York Inc. 1984
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-0-387-96037-1
  • eBook ISBN 978-1-4612-1116-7
  • Series ISSN 0066-5452
  • Edition Number 1
  • Number of Pages , 172
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Theoretical, Mathematical and Computational Physics
  • Buy this book on publisher's site
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