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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 Differential variational inequality ： ウィキペディア英語版 Differential variational inequality In mathematics, a differential variational inequality (DVI) is a dynamical system that incorporates ordinary differential equations and variational inequalities or complementarity problems. DVIs are useful for representing models involving both dynamics and inequality constraints. Examples of such problems include, for example, mechanical impact problems, electrical circuits with ''ideal'' diodes, Coulomb friction problems for contacting bodies, and dynamic economic and related problems such as dynamic traffic networks and networks of queues (where the constraints can either be upper limits on queue length or that the queue length cannot become negative). DVIs are related to a number of other concepts including differential inclusions, projected dynamical systems, evolutionary inequalities, and parabolic variational inequalities. Differential variational inequalities were first formally introduced by Pang and Stewart, whose definition should not be confused with the differential variational inequality used in Aubin and Cellina (1984). Differential variational inequalities have the form to find $u(t)\backslash in\; K$ such that : $\backslash langle\; v-u(t),\; F(t,x(t),u(t))\backslash rangle\backslash geq\; 0$ for every $v\backslash in\; K$ and almost all ''t''; ''K'' a closed convex set, where : $\backslash frac=f(t,x(t),u(t)),\backslash quad\; x(t\_0)\; =\; x\_0.$ Closely associated with DVIs are dynamic/differential complementarity problems: if ''K'' is a closed convex cone, then the variational inequality is equivalent to the complementarity problem: : $K\backslash ni\; u(t)\backslash quad\backslash perp\backslash quad\; F(t,x(t),u(t))\backslash in\; K^$ *. \, ==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「Differential variational inequality」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.