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

Released on by A. Majda
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  • Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables Book Detail

  • Author : A. Majda
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Science
  • Pages : 167
  • ISBN 13 : 1461211166
  • File Size : 52,52 MB
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Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables by A. Majda PDF Summary

Book Description: 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.

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