Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations

被引：42

作者：

Tahara, Hidetoshi ^{[1
]}

Yamazawa, Hiroshi ^{[2
]}

机构：

[1] Sophia Univ, Dept Informat & Commun Sci, Chiyoda Ku, Tokyo 1028554, Japan

[2] Shibaura Inst Technol, Coll Engineer & Design, Minuma Ku, Saitama 3378570, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 255卷 / 10期

基金：

日本学术振兴会;

关键词：

Multisummability; Formal solution; Non-Kowalevskian equation; Linear partial differential equation; POWER-SERIES SOLUTIONS; DIVERGENT SOLUTIONS; BOREL SUMMABILITY; VARIABLE-COEFFICIENTS; HYPERBOLIC-EQUATIONS;

D O I：

10.1016/j.jde.2013.07.061

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3592 / 3637

页数：46

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