Multisummability of formal power series solutions of nonlinear partial differential equations in complex domains

Article type: Research Article

Authors: Ōuchi, Sunao

Affiliations: Department of Mathematics, Sophia University, Kioicho Chiyoda-ku, Tokyo 102-8554, Japan E-mail: ouchi@mm.sophia.ac.jp; Fax +81 3 3238 3933

Abstract: Let $\hat{u}(t,x)=\sum_{n=1}^{\infty}u_{n}(x)t^{n},\ (t,x)\in \mathbb{C}\times \mathbb{C}^{d}$, be a formal power series solution of a nonlinear partial differential equation. We study multisummability of $\hat{u}(t,x)$. This paper is a continuation of [S. Ōuchi, Multisummability of formal solutions of some linear partial differential equations, J. Differential Equations 185 (2002), 513–549], where linear partial differential equations were treated.

Keywords: asymptotic expansion, formal power series solutions, multisummability

Journal: Asymptotic Analysis, vol. 47, no. 3-4, pp. 187-225, 2006