Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables (Paperback, Softcover reprint of the original 1st ed. 1984)

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."

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Applied Mathematical Sciences, 53
Release date:	June 1984
First published:	1984
Authors:	A. Majda
Dimensions:	235 x 155 x 9mm (L x W x T)
Format:	Paperback
Pages:	172
Edition:	Softcover reprint of the original 1st ed. 1984
ISBN-13:	978-0-387-96037-1
Categories:	Books > Science & Mathematics > Physics > General Books > Professional & Technical > Mechanical engineering & materials > Materials science > Mechanics of fluids > Hydraulics & pneumatics
LSN:	0-387-96037-6
Barcode:	9780387960371

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