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Applied Mathematical Sciences

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

Authors: Majda, A.

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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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-1-4612-1116-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
Authors
Series Title
Applied Mathematical Sciences
Series Volume
53
Copyright
1984
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1116-7
DOI
10.1007/978-1-4612-1116-7
Softcover ISBN
978-0-387-96037-1
Series ISSN
0066-5452
Edition Number
1
Number of Pages
172
Topics