Multisummability of Formal Power Series Solutions of Partial Differential Equations with Constant Coefficients
Multisummability of Formal Power Series Solutions of Partial Differential Equations with Constant Coefficients
复制标题
常系数偏微分方程形式幂级数解的多重可求性
DOI：
10.1016/j.jde.2004.02.002
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
W. Balser
中科院分区：
文献类型：
--
作者：
W. Balser
在作者较早的一篇论文中，研究了常系数偏微分方程。在方程的一定（限制性）假设下，刻画了相应柯西问题的归一化形式解可k求和的初始条件。这里我们处理一般情况，并证明了一个类似的结果，使用多重可和性代替k-可和性。适当的多重可和性类型仅取决于给定的偏微分方程，并且可以从相应的牛顿多边形中确定。
In an earlier paper of the author's, partial differential equations with constant coefficients have been studied. Under a certain (restrictive) assumption upon the equation, those initial conditions were characterized for which the normalized formal solution of a corresponding Cauchy problem is k-summable. Here we treat the general situation and prove an analogous result, using multisummability instead of k-summability. The appropriate multisummability type is shown to depend upon the given PDE only, and can be determined from a corresponding Newton polygon.