"\u7279\u5F81\u7EBF\u6CD5"@zh . . . "\u7279\u6027\u66F2\u7DDA\u6CD5"@ja . "17221"^^ . . "En math\u00E9matiques, la m\u00E9thode des caract\u00E9ristiques est une technique permettant de r\u00E9soudre les \u00E9quations aux d\u00E9riv\u00E9es partielles. Particuli\u00E8rement adapt\u00E9e aux probl\u00E8mes de transport, elle est utilis\u00E9e dans de nombreux domaines tels que la m\u00E9canique des fluides ou le transport de particules. Dans certains cas particuliers, la m\u00E9thode des caract\u00E9ristiques peut permettre la r\u00E9solution purement analytique de l'\u00E9quation aux d\u00E9riv\u00E9es partielles. Dans les cas plus complexes (rencontr\u00E9s par exemple en mod\u00E9lisation des syst\u00E8mes physiques), la m\u00E9thode des caract\u00E9ristiques peut \u00EAtre utilis\u00E9e comme une m\u00E9thode de r\u00E9solution num\u00E9rique du probl\u00E8me."@fr . . . . . . . . "\u6570\u5B66\u4E2D\u7684\u7279\u5F81\u7EBF\u6CD5\u662F\u6C42\u89E3\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u4E00\u79CD\u65B9\u6CD5\uFF0C\u9002\u7528\u4E8E\u51C6\u7EBF\u6027\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u6C42\u89E3\u3002\u53EA\u8981\u521D\u59CB\u503C\u4E0D\u662F\u6CBF\u7740\u7279\u5F81\u7EBF\u7ED9\u5B9A\uFF0C\u5373\u53EF\u901A\u8FC7\u7279\u5F81\u7EBF\u6CD5\u83B7\u5F97\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u7CBE\u786E\u89E3\u3002 \u5176\u57FA\u672C\u601D\u60F3\u662F\u901A\u8FC7\u628A\u53CC\u66F2\u7EBF\u578B\u7684\u51C6\u7EBF\u6027\u504F\u5FAE\u5206\u65B9\u7A0B\u8F6C\u5316\u4E3A\u4E24\u7EC4\u5E38\u5FAE\u5206\u65B9\u7A0B\uFF0C\u518D\u5BF9\u5E38\u5FAE\u5206\u65B9\u7A0B\u8FDB\u884C\u6C42\u89E3\u3002\u4E24\u7EC4\u5E38\u5FAE\u5206\u65B9\u7A0B\u4E2D\u7684\u4E00\u7EC4\u7528\u4E8E\u5B9A\u4E49\u7279\u5F81\u7EBF\uFF0C\u53E6\u4E00\u7EC4\u7528\u4EE5\u63CF\u8FF0\u89E3\u6CBF\u7ED9\u5B9A\u7279\u5F81\u7EBF\u53D8\u5316\u3002"@zh . . . . . . . "Die Methode der Charakteristiken ist eine Methode zur L\u00F6sung partieller Differentialgleichungen (PDGL/PDE), die typischerweise erster Ordnung und quasilinear sind, also Gleichungen vom Typ f\u00FCr eine Funktion mit der Anfangsbedingung . (Dabei hei\u00DFt eine Gleichung quasilinear, falls sie in den Ableitungen h\u00F6chster Ordnung linear ist). Charakteristiken spielen eine Rolle in der qualitativen Diskussion der L\u00F6sung bestimmter PDE und in der Frage, wann Anfangswertprobleme f\u00FCr diese PDE korrekt gestellt sind."@de . . "\uD574\uC11D\uD559\uC5D0\uC11C \uD2B9\uC131\uACE1\uC120\uBC95(\u7279\u6027\u66F2\u7DDA\u6CD5, \uC601\uC5B4: method of characteristics)\uC740 1\uCC28 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uC5F0\uB9BD 1\uCC28 \uC0C1\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC73C\uB85C \uD658\uC6D0\uD558\uC5EC \uD478\uB294 \uBC29\uBC95\uC774\uB2E4."@ko . . . "\u6570\u5B66\u4E2D\u7684\u7279\u5F81\u7EBF\u6CD5\u662F\u6C42\u89E3\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u4E00\u79CD\u65B9\u6CD5\uFF0C\u9002\u7528\u4E8E\u51C6\u7EBF\u6027\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u6C42\u89E3\u3002\u53EA\u8981\u521D\u59CB\u503C\u4E0D\u662F\u6CBF\u7740\u7279\u5F81\u7EBF\u7ED9\u5B9A\uFF0C\u5373\u53EF\u901A\u8FC7\u7279\u5F81\u7EBF\u6CD5\u83B7\u5F97\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u7CBE\u786E\u89E3\u3002 \u5176\u57FA\u672C\u601D\u60F3\u662F\u901A\u8FC7\u628A\u53CC\u66F2\u7EBF\u578B\u7684\u51C6\u7EBF\u6027\u504F\u5FAE\u5206\u65B9\u7A0B\u8F6C\u5316\u4E3A\u4E24\u7EC4\u5E38\u5FAE\u5206\u65B9\u7A0B\uFF0C\u518D\u5BF9\u5E38\u5FAE\u5206\u65B9\u7A0B\u8FDB\u884C\u6C42\u89E3\u3002\u4E24\u7EC4\u5E38\u5FAE\u5206\u65B9\u7A0B\u4E2D\u7684\u4E00\u7EC4\u7528\u4E8E\u5B9A\u4E49\u7279\u5F81\u7EBF\uFF0C\u53E6\u4E00\u7EC4\u7528\u4EE5\u63CF\u8FF0\u89E3\u6CBF\u7ED9\u5B9A\u7279\u5F81\u7EBF\u53D8\u5316\u3002"@zh . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u7279\u6027\u66F2\u7DDA\u6CD5\uFF08\u3068\u304F\u305B\u3044\u304D\u3087\u304F\u305B\u3093\u307B\u3046\u3001\u82F1: method of characteristics\uFF09\u3068\u306F\u3001\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u5BFE\u3059\u308B\u4E00\u3064\u306E\u89E3\u6CD5\u3067\u3042\u308B\u3002\u4E00\u822C\u306B\u306F\u4E00\u968E\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u5BFE\u3057\u3066\u9069\u7528\u3055\u308C\u308B\u304C\u3001\u4EFB\u610F\u306E\u53CC\u66F2\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u5BFE\u3059\u308B\u3088\u308A\u4E00\u822C\u306E\u7279\u6027\u66F2\u7DDA\u6CD5\u3082\u5B58\u5728\u3059\u308B\u3002\u3053\u306E\u65B9\u6CD5\u3067\u306F\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3092\u3001\u5E38\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306E\u65CF\u306B\u66F8\u304D\u4E0B\u3057\u3001\u9069\u5207\u306A\u8D85\u66F2\u9762\u4E0A\u3067\u4E0E\u3048\u3089\u308C\u305F\u3044\u304F\u3064\u304B\u306E\u521D\u671F\u30C7\u30FC\u30BF\u3088\u308A\u7A4D\u5206\u3055\u308C\u308B\u3053\u3068\u306B\u3088\u3063\u3066\u305D\u306E\u7DDA\u306B\u6CBF\u3063\u305F\u89E3\u304C\u5F97\u3089\u308C\u308B\u3002"@ja . . . . . . . . . . . "\u041C\u0435\u0442\u043E\u0434 \u0445\u0430\u0440\u0430\u043A\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043A"@ru . . "\u041C\u0435\u0442\u043E\u0434 \u0445\u0430\u0440\u0430\u043A\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043A"@uk . "In matematica, il metodo delle caratteristiche \u00E8 un importante strumento utile per risolvere le equazioni differenziali alle derivate parziali (PDE) di primo grado, ed in generale si applica a tutte le equazioni iperboliche. Ad esempio, se si ha un'equazione del tipo: ponendo si ha: da cui: Si tratta di un sistema di equazioni differenziali ordinarie, e le prime due relazioni sono dette curve caratteristiche dell'equazione. Integrando si ottiene: con costante di integrazione. Tale metodo si applica, ad esempio, all'equazione delle onde e all'equazione del trasporto."@it . . . "In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partial differential equation. The method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data given on a suitable hypersurface."@en . . "\u041C\u0435\u0442\u043E\u0434 \u0445\u0430\u0440\u0430\u043A\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043A \u2014 \u043C\u0435\u0442\u043E\u0434 \u0440\u0435\u0448\u0435\u043D\u0438\u044F \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445. \u041E\u0431\u044B\u0447\u043D\u043E \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u0435\u0442\u0441\u044F \u043A \u0440\u0435\u0448\u0435\u043D\u0438\u044E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445 \u043F\u0435\u0440\u0432\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430, \u043D\u043E \u043E\u043D \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u043F\u0440\u0438\u043C\u0435\u043D\u0435\u043D \u0438 \u043A \u0440\u0435\u0448\u0435\u043D\u0438\u044E \u0433\u0438\u043F\u0435\u0440\u0431\u043E\u043B\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0431\u043E\u043B\u0435\u0435 \u0432\u044B\u0441\u043E\u043A\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430."@ru . . . . . . . . . . . . . . . . "Die Methode der Charakteristiken ist eine Methode zur L\u00F6sung partieller Differentialgleichungen (PDGL/PDE), die typischerweise erster Ordnung und quasilinear sind, also Gleichungen vom Typ f\u00FCr eine Funktion mit der Anfangsbedingung . (Dabei hei\u00DFt eine Gleichung quasilinear, falls sie in den Ableitungen h\u00F6chster Ordnung linear ist). Die grundlegende Idee besteht darin, die PDE durch eine geeignete Koordinatentransformation auf ein System gew\u00F6hnlicher Differentialgleichungen auf bestimmten Hyperfl\u00E4chen, sogenannten Charakteristiken, zur\u00FCckzuf\u00FChren.Die PDE kann dann als Anfangswertproblem in dem neuen System mit Anfangswerten auf den die Charakteristik schneidenden Hyperfl\u00E4chen gel\u00F6st werden.St\u00F6rungen breiten sich l\u00E4ngs der Charakteristiken aus.Die Methode kann auch allgemein auf hyperbolische partielle Differentialgleichungen angewandt werden, deren Prototyp die Wellengleichung ist, und auf einige weitere PDEs h\u00F6herer Ordnung. Charakteristiken spielen eine Rolle in der qualitativen Diskussion der L\u00F6sung bestimmter PDE und in der Frage, wann Anfangswertprobleme f\u00FCr diese PDE korrekt gestellt sind. Die Methode geht auf Joseph-Louis Lagrange zur\u00FCck (1779, quasilineare partielle Differentialgleichungen erster Ordnung). Sie wurde 1784 von Gaspard Monge geometrisch begr\u00FCndet, was Johann Friedrich Pfaff 1815 und Augustin-Louis Cauchy 1819 auf mehr als zwei Dimensionen erweiterten."@de . . . . . "Methode der Charakteristiken"@de . "1116650383"^^ . "M\u00E9thode des caract\u00E9ristiques"@fr . . "\u041C\u0435\u0442\u043E\u0434 \u0445\u0430\u0440\u0430\u043A\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043A (\u0430\u043D\u0433\u043B. Method of characteristics) - \u043C\u0435\u0442\u043E\u0434 \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u044F \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C \u0443 \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445. \u0417\u0430\u0437\u0432\u0438\u0447\u0430\u0439 \u0437\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0434\u043E \u0440\u0456\u0432\u043D\u044F\u043D\u044C \u0443 \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u043F\u0435\u0440\u0448\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0443, \u043F\u0440\u043E\u0442\u0435 \u043C\u043E\u0436\u0435 \u0431\u0443\u0442\u0438 \u0437\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0430\u043D\u0438\u043C \u0456 \u0434\u043E \u0433\u0456\u043F\u0435\u0440\u0431\u043E\u043B\u0456\u0447\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C \u0432\u0438\u0449\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0443. \u041C\u0435\u0442\u043E\u0434 \u043F\u043E\u043B\u044F\u0433\u0430\u0454 \u0443 \u043F\u0440\u0438\u0432\u0435\u0434\u0435\u043D\u043D\u0456 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0443 \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u0434\u043E \u0441\u0456\u043C\u0435\u0439\u0441\u0442\u0432\u0430 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u0438\u0445 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B\u044C\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C."@uk . . "\uD2B9\uC131\uACE1\uC120\uBC95"@ko . "Method of characteristics"@en . "De methode van karakteristieken is een wiskundige techniek voor het oplossen van parti\u00EBle differentiaalvergelijkingen (PDV). Een PDV beschrijft een ontwikkeling die afhangt van verschillende omstandigheden (variabelen). De methode is van toepassing op zogenaamde en . De PDV wordt vereenvoudigd tot een schaar van gewone differentiaalvergelijkingen, die integratie toelaten uitgaand van beginwaarden op een geschikt hyperoppervlak."@nl . "Methode van karakteristieken"@nl . . . . . "\u041C\u0435\u0442\u043E\u0434 \u0445\u0430\u0440\u0430\u043A\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043A \u2014 \u043C\u0435\u0442\u043E\u0434 \u0440\u0435\u0448\u0435\u043D\u0438\u044F \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445. \u041E\u0431\u044B\u0447\u043D\u043E \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u0435\u0442\u0441\u044F \u043A \u0440\u0435\u0448\u0435\u043D\u0438\u044E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445 \u043F\u0435\u0440\u0432\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430, \u043D\u043E \u043E\u043D \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u043F\u0440\u0438\u043C\u0435\u043D\u0435\u043D \u0438 \u043A \u0440\u0435\u0448\u0435\u043D\u0438\u044E \u0433\u0438\u043F\u0435\u0440\u0431\u043E\u043B\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0431\u043E\u043B\u0435\u0435 \u0432\u044B\u0441\u043E\u043A\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430."@ru . . . . . . . . "In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partial differential equation. The method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data given on a suitable hypersurface."@en . "En math\u00E9matiques, la m\u00E9thode des caract\u00E9ristiques est une technique permettant de r\u00E9soudre les \u00E9quations aux d\u00E9riv\u00E9es partielles. Particuli\u00E8rement adapt\u00E9e aux probl\u00E8mes de transport, elle est utilis\u00E9e dans de nombreux domaines tels que la m\u00E9canique des fluides ou le transport de particules."@fr . "\u6570\u5B66\u306B\u304A\u3044\u3066\u7279\u6027\u66F2\u7DDA\u6CD5\uFF08\u3068\u304F\u305B\u3044\u304D\u3087\u304F\u305B\u3093\u307B\u3046\u3001\u82F1: method of characteristics\uFF09\u3068\u306F\u3001\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u5BFE\u3059\u308B\u4E00\u3064\u306E\u89E3\u6CD5\u3067\u3042\u308B\u3002\u4E00\u822C\u306B\u306F\u4E00\u968E\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u5BFE\u3057\u3066\u9069\u7528\u3055\u308C\u308B\u304C\u3001\u4EFB\u610F\u306E\u53CC\u66F2\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u5BFE\u3059\u308B\u3088\u308A\u4E00\u822C\u306E\u7279\u6027\u66F2\u7DDA\u6CD5\u3082\u5B58\u5728\u3059\u308B\u3002\u3053\u306E\u65B9\u6CD5\u3067\u306F\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3092\u3001\u5E38\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306E\u65CF\u306B\u66F8\u304D\u4E0B\u3057\u3001\u9069\u5207\u306A\u8D85\u66F2\u9762\u4E0A\u3067\u4E0E\u3048\u3089\u308C\u305F\u3044\u304F\u3064\u304B\u306E\u521D\u671F\u30C7\u30FC\u30BF\u3088\u308A\u7A4D\u5206\u3055\u308C\u308B\u3053\u3068\u306B\u3088\u3063\u3066\u305D\u306E\u7DDA\u306B\u6CBF\u3063\u305F\u89E3\u304C\u5F97\u3089\u308C\u308B\u3002"@ja . . . . . "De methode van karakteristieken is een wiskundige techniek voor het oplossen van parti\u00EBle differentiaalvergelijkingen (PDV). Een PDV beschrijft een ontwikkeling die afhangt van verschillende omstandigheden (variabelen). De methode is van toepassing op zogenaamde en . De PDV wordt vereenvoudigd tot een schaar van gewone differentiaalvergelijkingen, die integratie toelaten uitgaand van beginwaarden op een geschikt hyperoppervlak."@nl . . "In matematica, il metodo delle caratteristiche \u00E8 un importante strumento utile per risolvere le equazioni differenziali alle derivate parziali (PDE) di primo grado, ed in generale si applica a tutte le equazioni iperboliche. Ad esempio, se si ha un'equazione del tipo: ponendo si ha: da cui: Si tratta di un sistema di equazioni differenziali ordinarie, e le prime due relazioni sono dette curve caratteristiche dell'equazione. Integrando si ottiene: con costante di integrazione. Tale metodo si applica, ad esempio, all'equazione delle onde e all'equazione del trasporto."@it . "Metodo delle caratteristiche"@it . "751933"^^ . "\uD574\uC11D\uD559\uC5D0\uC11C \uD2B9\uC131\uACE1\uC120\uBC95(\u7279\u6027\u66F2\u7DDA\u6CD5, \uC601\uC5B4: method of characteristics)\uC740 1\uCC28 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uC5F0\uB9BD 1\uCC28 \uC0C1\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC73C\uB85C \uD658\uC6D0\uD558\uC5EC \uD478\uB294 \uBC29\uBC95\uC774\uB2E4."@ko . "\u041C\u0435\u0442\u043E\u0434 \u0445\u0430\u0440\u0430\u043A\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043A (\u0430\u043D\u0433\u043B. 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