The Asymptotic Behavior of Singular Solutions of Some Nonlinear Partial Differential Equations in the Complex Domain

Abstract

Let $u(t,x)$ ($(t,x)\in C\times C^d$) be a solution of a nonlinear partial differential equation in a neighborhood of the origin, which is not necessarily holomorphic on $\{t=0\}$. We study the asymptotic behavior of $u(t,x)$ as $t\to 0$ and give its asymptotic terms with remainder estimate of Gevrey type.