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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Burgers equation ： ウィキペディア英語版 Burgers' equation Burgers' equation is a fundamental partial differential equation occurring in various areas of applied mathematics, such as fluid mechanics,〔It relates to the Navier-Stokes momentum equation with the pressure term removed : here the variable is the flow speed y=u〕 nonlinear acoustics,〔It arises from Westervelt equation with an assumption of strictly forward propagating waves and the use of a coordinate transformation to a retarded time frame: here the variable is the pressure〕 gas dynamics, traffic flow. It is named for Johannes Martinus Burgers (1895–1981). For a given field $y(x,t)$ and diffusion coefficient (or ''viscosity'', as in the original fluid mechanical context) $d$, the general form of Burgers' equation (also known as viscous Burgers' equation) in one space dimension is the dissipative system: :$\backslash frac\; +\; y\; \backslash frac\; =\; d\; \backslash frac$. Added space-time noise $\backslash eta(x,t)$ forms a stochastic Burgers' equation〔W. Wang and A. J. Roberts. Diffusion approximation for self-similarity of stochastic advection in Burgers’ equation. ''Communications in Mathematical Physics'', July 2014.〕 :$\backslash frac\; +\; y\; \backslash frac\; =\; d\; \backslash frac-\backslash lambda\backslash frac$ This stochastic PDE is equivalent to the Kardar-Parisi-Zhang equation in a field $h(x,t)$ upon substituting $y(x,t)=-\backslash lambda\backslash partial\; h/\backslash partial\; x$. But whereas Burgers' equation only applies in one spatial dimension, the Kardar-Parisi-Zhang equation generalises to multiple dimensions. When the diffusion term is absent (i.e. d=0), Burgers' equation becomes the inviscid Burgers' equation: :$\backslash frac\; +\; y\; \backslash frac\; =\; 0,$ which is a prototype for conservation equations that can develop discontinuities (shock waves). The previous equation is the 'advection form' of the Burgers' equation. The 'conservation form' is :$\backslash frac\; +\; \backslash frac\backslash frac\backslash big(y^2\backslash big)\; =\; 0.$ == Solution == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Burgers' equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.