Series: Applied Mathematical Sciences. Num Pages: 172 pages, biography. BIC Classification: PH; TGMF2. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 9. Weight in Grams: 550. . 1984. Softcover reprint of the original 1st ed. 1984. paperback. . . . . Books ship from the US and Ireland.

N� de ref. del art�culo V9780387960371

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Detalles bibliogr�ficos

T�tulo: Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
Editor: Springer
Fecha de publicaci�n: 1984
Idioma: Ingl�s
ISBN 10: 0387960376
ISBN 13: 9780387960371
Encuadernaci�n: Encuadernaci�n de tapa blanda
Estado: New

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Sinopsis

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.

Rese�a del editor

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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