Envelopes of families of framed surfaces and singular solutions of first-order partial differential equations
Envelopes of families of framed surfaces and singular solutions of first-order partial differential equations
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框架曲面族的包络和一阶偏微分方程的奇异解
DOI：
10.1017/prm.2020.71
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Yu Haiou
中科院分区：
文献类型：
--
作者：
Takahashi Masatomo;Yu Haiou
为了研究奇异曲面的包络，我们分别引入了单参数族和双参数族以及基本不变量。利用基本不变量，给出了单参数族和双参数曲面族的存在唯一性定理。然后定义了单参数族和双参数族的包络，给出了包络存在的条件，称为包络定理。作为包络定理的应用，我们证明了完全可积一阶偏微分方程奇异解的投影是包络。
In order to investigate envelopes for singular surfaces, we introduce one- and two-parameter families of framed surfaces and the basic invariants, respectively. By using the basic invariants, the existence and uniqueness theorems of one- and two-parameter families of framed surfaces are given. Then we define envelopes of one- and two-parameter families of framed surfaces and give the existence conditions of envelopes which are called envelope theorems. As an application of the envelope theorems, we show that the projections of singular solutions of completely integrable first-order partial differential equations are envelopes.
DOI：
10.1142/9108
发表时间：
2015-12
期刊：
--
影响因子：
--
作者：
S. Izumiya;M. Fuster;M. Ruas;F. Tari
通讯作者：
S. Izumiya;M. Fuster;M. Ruas;F. Tari
一阶偏微分方程完全可积的表征
影响因子：
0.7
作者：
S. Izumiya
通讯作者：
S. Izumiya
影响因子：
0.9
作者：
V. Lychagin
通讯作者：
V. Lychagin