[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki29\/archives\/106247#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki29\/archives\/106247","headline":"\u5fae\u5206\u5305\u542b\u5f0f – Wikipedia","name":"\u5fae\u5206\u5305\u542b\u5f0f – Wikipedia","description":"\u5fae\u5206\u5305\u542b\u5f0f\u3068\u306f\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u8003\u3048\u65b9\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002 dxdt(t)\u2208F(t,x(t)),{displaystyle {frac {dx}{dt}}(t)in F(t,x(t)),} \u3053\u3053\u3067 F(t, x) \u306f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u306f\u591a\u6b21\u5143\u7a7a\u9593\u5185\u306e\u70b9 Rd{displaystyle scriptstyle {mathbb {R} }^{d}} \u3060\u304c\u3001\u5fae\u5206\u5305\u542b\u5f0f\u306b\u304a\u3044\u3066\u306f\u96c6\u5408\u3067\u3042\u308b\u3002\u5fae\u5206\u5305\u542b\u5f0f\u306f\u3001\u5fae\u5206\u5909\u5206\u4e0d\u7b49\u5f0f (differential variational inequality, en)\u3001projected dynamical","datePublished":"2022-03-23","dateModified":"2022-03-23","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki29\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki29\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/fa4a76d015ecc071ceb5491d8708649b76258e06","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/fa4a76d015ecc071ceb5491d8708649b76258e06","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki29\/archives\/106247","about":["Wiki"],"wordCount":2028,"articleBody":"\u5fae\u5206\u5305\u542b\u5f0f\u3068\u306f\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u8003\u3048\u65b9\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002  dxdt(t)\u2208F(t,x(t)),{displaystyle {frac {dx}{dt}}(t)in F(t,x(t)),}\u3053\u3053\u3067 F(t, x) \u306f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u306f\u591a\u6b21\u5143\u7a7a\u9593\u5185\u306e\u70b9   Rd{displaystyle scriptstyle {mathbb {R} }^{d}} \u3060\u304c\u3001\u5fae\u5206\u5305\u542b\u5f0f\u306b\u304a\u3044\u3066\u306f\u96c6\u5408\u3067\u3042\u308b\u3002\u5fae\u5206\u5305\u542b\u5f0f\u306f\u3001\u5fae\u5206\u5909\u5206\u4e0d\u7b49\u5f0f (differential variational inequality, en)\u3001projected dynamical system\u3001\u30af\u30fc\u30ed\u30f3\u306e\u52d5\u6469\u64e6\u529b\u3001\u30d5\u30a1\u30b8\u30a3\u96c6\u5408\u8ad6\u306a\u3069\u306e\u5206\u91ce\u3067\u4f7f\u308f\u308c\u3066\u3044\u308b\u3002\u305f\u3068\u3048\u3070\u3001\u30af\u30fc\u30ed\u30f3\u306b\u3088\u308b\u52d5\u6469\u64e6\u529b\u306e\u6cd5\u5247\u3067\u306f\u3001\u7269\u4f53\u306e\u91cd\u3055\u3092 N\u3001\u6469\u64e6\u4fc2\u6570\u3092 \u03bc \u3068\u3059\u308b\u3068\u304d\u3001\u6469\u64e6\u529b\u306f\u7269\u4f53\u306e\u52d5\u3044\u3066\u3044\u308b\u65b9\u5411\u3068\u9006\u5411\u304d\u306b  \u03bcN \u3068\u3044\u3046\u5927\u304d\u3055\u3067\u751f\u3058\u308b\u3002\u3057\u304b\u3057\u3001\u3059\u3079\u308a\u304c\u751f\u3058\u3066\u3044\u306a\u3044\u3068\u304d\u306b\u306f\u3001\u6469\u64e6\u529b\u306f\u5e73\u9762\u5185\u3067\u5927\u304d\u3055\u304c \u03bcN \u4ee5\u4e0b\u306e\u3069\u3093\u306a\u30d9\u30af\u30c8\u30eb\u306b\u306a\u3063\u3066\u3082\u3088\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u6469\u64e6\u529b\u3092\u4f4d\u7f6e\u3068\u901f\u5ea6\u306e\u95a2\u6570\u3068\u3057\u3066\u8868\u305d\u3046\u3068\u3059\u308b\u3068\u3001\u305d\u306e\u95a2\u6570\u306e\u53d6\u308b\u306e\u306f\u5024\u3067\u306f\u306a\u304f\u96c6\u5408\u3068\u306a\u308b\u3002\u89e3\u306e\u5b58\u5728\u3092\u8003\u3048\u308b\u3068\u304d\u306f\u901a\u5e38\u3001F(t,\u00a0x) \u304c x \u3068 \u53ef\u6e2c\u306at \u306e\u534a\u9023\u7d9a (hemicontinuous \u307e\u305f\u306f upper semi-continuous, en) \u306a\u95a2\u6570\u3067\u3001F(t,\u00a0x) \u306f\u3059\u3079\u3066\u306e t and x \u306b\u3064\u3044\u3066\u9589\u3058\u3066\u3044\u308b\u51f8\u96c6\u5408\u3067\u3042\u308b\u3053\u3068\u304c\u524d\u63d0\u3067\u3042\u308b\u3002\u521d\u671f\u5024\u554f\u984c  dxdt(t)\u2208F(t,x(t)),x(t0)=x0{displaystyle {frac {dx}{dt}}(t)in F(t,x(t)),quad x(t_{0})=x_{0}}\u306e\u89e3\u306f\u3001\u5341\u5206\u306b\u77ed\u3044\u6642\u9593 [t0,\u00a0t0\u00a0+\u00a0\u03b5)\u3000(\u3053\u3053\u3067 \u03b5\u00a0>\u00a00) \u3067\u306f\u5b58\u5728\u3059\u308b\u3002\u307e\u305f F \u304c\u767a\u6563\u3057\u306a\u3044 (\u2016x(t)\u2016\u2192\u221e{displaystyle scriptstyle Vert x(t)Vert ,to ,infty } as t\u2192t\u2217{displaystyle scriptstyle t,to ,t^{*}} for a finite t\u2217{displaystyle scriptstyle t^{*}}) \u5834\u5408\u306f\u3001\u5927\u57df\u7684\u306a\u89e3\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u308b\u3002\u51f8\u96c6\u5408\u3067\u306a\u3044\u5fae\u5206\u5305\u542b\u5f0f F(t,\u00a0x) \u306e\u89e3\u306e\u5b58\u5728\u5b9a\u7406\u306f\u73fe\u5728\u3001\u660e\u3089\u304b\u306b\u3055\u308c\u3066\u3044\u306a\u3044\u3002\u89e3\u306e\u4e00\u610f\u6027\u3092\u793a\u3059\u306b\u306f\u3001\u901a\u5e38\u4ed6\u306e\u6761\u4ef6\u304c\u5fc5\u8981\u3068\u306a\u308b\u3002\u305f\u3068\u3048\u3070\u95a2\u6570 F(t,x){displaystyle F(t,x)} \u306b\u304a\u3044\u3066\u7247\u5074\u30ea\u30d7\u30b7\u30c3\u30c4\u6761\u4ef6(x1\u2212x2)T(F(t,x1)\u2212F(t,x2))\u2264C\u2016x1\u2212x2\u20162{displaystyle (x_{1}-x_{2})^{T}(F(t,x_{1})-F(t,x_{2}))leq CVert x_{1}-x_{2}Vert ^{2}}\u3092\u3059\u3079\u3066\u306e x1 and x2 \u306b\u3064\u3044\u3066\u6e80\u305f\u3059\u3088\u3046\u306a C \u304c\u3042\u308b\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001\u521d\u671f\u5024\u554f\u984cdxdt(t)\u2208F(t,x(t)),x(t0)=x0{displaystyle {frac {dx}{dt}}(t)in F(t,x(t)),quad x(t_{0})=x_{0}}\u306e\u89e3\u306f\u4e00\u610f\u306b\u5b9a\u307e\u308b\u3002\u3053\u308c\u306f\u30df\u30f3\u30c6\u30a3 (G. J. Minty) \u3068 \u30d6\u30ec\u30b8\u30b9 (H. Brezis, en) \u306b\u3088\u308b maximal monotone operators \u3068\u3082\u6df1\u304f\u95a2\u308f\u3063\u3066\u3044\u308b\u3002\u5fae\u5206\u5305\u542b\u5f0f\u306f\u4e0d\u9023\u7d9a\u306a\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u6790\u3059\u308b\u306e\u306b\u7528\u3044\u3089\u308c\u308b\u3002\u305f\u3068\u3048\u3070\u6a5f\u68b0\u5de5\u5b66\u5206\u91ce\u3067\u306e\u30af\u30fc\u30ed\u30f3\u306e\u6469\u64e6\u529b\u3084\u96fb\u529b\u5206\u91ce\u3067\u306e\u6700\u9069\u306a\u30b9\u30a4\u30c3\u30c1\u30f3\u30b0\u306e\u89e3\u6790\u306a\u3069\u3067\u3042\u308b\u3002\u307e\u305f\u30d5\u30a3\u30ea\u30dd\u30d5 (A. F. Filippov, 1960) \u306b\u3088\u308b\u4e0d\u9023\u7d9a\u306a\u65b9\u7a0b\u5f0f\u306e\u6b63\u5247\u5316\u304c\u91cd\u8981\u306a\u8ca2\u732e\u3068\u3057\u3066\u6319\u3052\u3089\u308c\u308b\u3002\u30b2\u30fc\u30e0\u7406\u8ad6\u306b\u304a\u3051\u308b\u5fae\u5206\u30b2\u30fc\u30e0 (differential game, en) \u306b\u304a\u3051\u308b\u30af\u30e9\u30bd\u30d5\u30b9\u30ad\u30a4 (Nikolai Nikolaevich Krasovsky, en) \u306b\u3088\u308b\u6b63\u5247\u5316\u6cd5\u3082\u4f7f\u308f\u308c\u305f\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Jean-Pierre Aubin, Arrigo Cellina Differential Inclusions, Set-Valued Maps And Viability Theory, Grundl. der Math. Wiss., vol. 264, Springer – Verlag, Berlin, 1984J.-P. Aubin and H. Frankowska Set-Valued Analysis, Birkh\u00a8auser, Basel, 1990Klaus Deimling Multivalued Differential Equations, Walter de Gruyter, 1992J. Andres, L. G\u00f3rniewicz Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers, 2003\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki29\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki29\/archives\/106247#breadcrumbitem","name":"\u5fae\u5206\u5305\u542b\u5f0f – Wikipedia"}}]}]