Isbn: 9780387960371 - compressible fluid flow and systems of conservation laws in several space variables (applied mathematical sciences, 53, band 53) (2 Ergebnisse)

Zustand: New. In.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. …