### Abstract

The paper considers the Cauchy problem for linear partial differential equations of non-Kowalevskian type in the complex domain. It is shown that if the Cauchy data are entire functions of a suitable order, the problem has a formal solution which is multisummable. The precise bound of the admissible order of entire functions is described in terms of the Newton polygon of the equation.

Original language | English |
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Pages (from-to) | 3592-3637 |

Number of pages | 46 |

Journal | Journal of Differential Equations |

Volume | 255 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2013 Nov 15 |

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### Keywords

- Formal solution
- Linear partial differential equation
- Multisummability
- Non-Kowalevskian equation
- Primary
- Secondary

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics