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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables

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

Majda, A.

Paperback

Series: Applied Mathematical Sciences, Book 53

Technology & EngineeringGeneral GardeningGeneral Mathematics

ISBN10: 0387960376
ISBN13: 9780387960371
Publisher: Springer Nature
Published: Jun 20 1984
Pages: 172
Weight: 0.55
Height: 0.37 Width: 6.14 Depth: 9.21
Language: English
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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