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 ...
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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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New in new dust jacket. Trade paperback (US). Glued binding. 172 p. Contains: Illustrations, black & white. Springer Series on Environmental Management, 53. Audience: General/trade. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service.
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1984, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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