{"product_id":"compressible-fluid-flow-and-systems-of-conservation-laws-in-several-space-variables-9780387960371","title":"Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables","description":"\u003cp\u003e • Author(s): A. Majda\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eConservation 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 \u0026gt; 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45280671334551,"sku":"9780387960371","price":10283.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780387960371.webp?v=1769296983","url":"https:\/\/atlanticbooks.com\/products\/compressible-fluid-flow-and-systems-of-conservation-laws-in-several-space-variables-9780387960371","provider":"Atlantic Books","version":"1.0","type":"link"}