Holomorphic and singular solutions of nonlinear singular first order partial differential equations
Holomorphic and singular solutions of nonlinear singular first order partial differential equations
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DOI：
10.2977/prims/1195170572
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发表时间：
1990-12
影响因子：
1.2
通讯作者：
R. Gérard;H. Tahara
中科院分区：
文献类型：
--
作者：
R. Gérard;H. Tahara
在本章中，我们将讨论以下类型的非线性奇异一阶偏微分方程$$t{{\partial u} \over {\partial t}} = F\left( {t,x,u,{{\partial u} \over {\partial x}}} \right)$$(5.0.1)，其中\((t,x) \in {\cal C_t} \times {({\cal C_x})^n},x = ({x_1}, \ldots ,{x_n}),{{\partial u} \over {\partial x}} = ({{\partial u} \over {\partial {x_1}}}, \ldots ,{{\partial u} \over {\partial {x_n}}}),F(t,x,u,v)\)是在以\({\cal C_t} \times {({\cal C_x})^n} \times {\cal C_u} \times {({\cal C_v})^n}\)原点为中心的多盘Δ中定义的函数，以及\(v = ({v_1}, \ldots ,{v_n})\)。用\({\Delta _0} \cap \{ t = 0,u = 0,v = 0\}\)表示。
In this chapter, we will discuss the following types of non linear singular first order partial differential equations $$t{{\partial u} \over {\partial t}} = F\left( {t,x,u,{{\partial u} \over {\partial x}}} \right)$$ (5.0.1) where \((t,x) \in {\cal C_t} \times {({\cal C_x})^n},x = ({x_1}, \ldots ,{x_n}),{{\partial u} \over {\partial x}} = ({{\partial u} \over {\partial {x_1}}}, \ldots ,{{\partial u} \over {\partial {x_n}}}),F(t,x,u,v)\) is a function defined in a polydisk Δ centered at the origin of \({\cal C_t} \times {({\cal C_x})^n} \times {\cal C_u} \times {({\cal C_v})^n}\), and \(v = ({v_1}, \ldots ,{v_n})\). Let us denote \({\Delta _0} \cap \{ t = 0,u = 0,v = 0\}\).