Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations
Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations
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某些线性偏微分方程柯西问题形式解的多重可求性
DOI：
10.1016/j.jde.2013.07.061
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发表时间：
2013
影响因子：
2.4
通讯作者：
H. Tahara and H. Yamazawa
中科院分区：
文献类型：
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作者：
本田あおい;岡崎悦明;佐藤坦;渡辺一雄;Makoto Masumoto;Kiyoshi Mochizuki;R. Kajikiya;本田あおい,岡崎悦明,佐藤 坦;H. Tahara and H. Yamazawa
本文考虑复域上非科瓦列夫斯基类型的线性偏微分方程柯西问题。证明了如果柯西数据是适当阶的整函数，则该问题有一个形式解，该解是可重和的。用方程的牛顿多边形描述了整函数可容许级的精确界。
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.