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

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

Advertisement

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

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.

Erhaltungssatz Gasdynamik Kompressible Strömung Stosswelle Systems flow

- 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
- Print ISBN 978-0-387-96037-1
- Online ISBN 978-1-4612-1116-7
- Series Print ISSN 0066-5452
- Buy this book on publisher's site