Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
Authors: Majda, A.
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- About this book
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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)
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Introduction
Pages 1-29
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Smooth Solutions and the Equations of Incompressible Fluid Flow
Pages 30-80
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The Formation of Shock Waves in Smooth Solutions
Pages 81-110
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The Existence and Stability of Shock Fronts in Several Space Variables
Pages 111-156
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Table of contents (4 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
- Authors
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- A. Majda
- 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
