高维复域中具非正则奇异性的非线性偏微分方程的形式解

Formal Solutions for First Order Nonlinear PDE with Irregular Singularity in High Dimensional Complex Domain

本文在C_t×C_x^n上研究一类一阶具非正则奇异性的非线性偏微分方程.在一定条件下,证明了其形式幂级数解属于形式Gevrey类,并给出了其Gevrey类指标的精确刻画.

In this paper, we study a class of first order nonlinear partial differential equation with irregular singularity in the domain Ct×Cx^n. Under certain assumptions, we prove the existence and uniqueness of the formal solution in formal Gevrey class.