# Decomposition of Solutions of the Cauchy Problem of a Quasi-Homogeneous Partial Differential Equation

### Kunio Ichinobe

Aichi University of Education, Kariya City (Aichi), Japan### Masatake Miyake

Nagoya University, Japan

## Abstract

We give a decomposition formula for the formal solution of the Cauchy problem for a quasi-homogeneous partial differential equation with constant coecients in the two-dimensional complex plane. The decomposition formula, Theorem 1.1, is given in a form associated with the factorization of the relevant operator which is similar to the decomposition of the solution of an ordinary differential equation with constant coefficients.

## Cite this article

Kunio Ichinobe, Masatake Miyake, Decomposition of Solutions of the Cauchy Problem of a Quasi-Homogeneous Partial Differential Equation. Publ. Res. Inst. Math. Sci. 48 (2012), no. 2, pp. 373–388

DOI 10.2977/PRIMS/72