翻訳と辞書 Words near each other ・ WealthTrust ・ Wealthwood Township, Aitkin County, Minnesota ・ Wealthwood, Minnesota ・ Wealthy (apple) ・ Weak convergence ・ Weak convergence (Hilbert space) ・ Weak derivative ・ Weak dimension ・ Weak duality ・ Weak entity ・ Weak equivalence ・ Weak equivalence (homotopy theory) ・ Weak evolutionarily stable strategy ・ Weak focusing ・ Weak form and strong form ・ Weak formulation ・ Weak generative capacity ・ Weak gravitational lensing ・ Weak Hausdorff space ・ Weak heap ・ Weak Hopf algebra ・ Weak hypercharge ・ Weak in the Presence of Beauty ・ Weak in the Presence of Beauty (album) ・ Weak in the Presence of Beauty (song) ・ Weak inflection ・ Weak interaction ・ Weak interpretability ・ Weak inverse ・ Weak isospin Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Weak formulation ： ウィキペディア英語版 Weak formulation Weak formulations are an important tool for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". This is equivalent to formulating the problem to require a solution in the sense of a distribution. We introduce weak formulations by a few examples and present the main theorem for the solution, the Lax–Milgram theorem. ==General concept== Let $V$ be a Banach space. We want to find the solution $u\; \backslash in\; V$ of the equation :$Au\; =\; f$, where $A:V\backslash to\; V\text{'}$ and $f\backslash in\; V\text{'}$, with $V\text{'}$ being the dual of $V$. Calculus of variations tells us that this is equivalent to finding $u\backslash in\; V$ such that for all $v\backslash in\; V$ holds: :$()(v)\; =\; f(v)$. Here, we call $v$ a test vector or test function. We bring this into the generic form of a weak formulation, namely, find $u\backslash in\; V$ such that :$a(u,v)\; =\; f(v)\; \backslash quad\; \backslash forall\; v\backslash in\; V,$ by defining the bilinear form :$a(u,v)\; :=\; ()(v).$ Since this is very abstract, let us follow this by some examples. 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「Weak formulation」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.