{"product_id":"9780387960371","title":"Applied Mathematical Sciences","description":"\u003ch1\u003eApplied Mathematical Sciences\u003c\/h1\u003e \u003ch2\u003eMajda, A.\u003c\/h2\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 \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1984-06-20\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387960371\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4612-1116-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 172\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":44422339526796,"sku":"9780387960371","price":143.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387960371.jpg?v=1775729625","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780387960371","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}