Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients

被引：17

作者：

Michalik, S. ^{[1
]}

机构：

[1] Cardinal Stefan Wyszynski Univ, Coll Sci, Fac Math & Nat Sci, Warsaw, Poland

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2012年 / 18卷 / 01期

关键词：

Fractional linear PDEs with constant coefficients; formal power series; Borel summability; multisummability; Duhamel principle; POWER-SERIES SOLUTIONS; DIVERGENT SOLUTIONS; SUMMABILITY;

D O I：

10.1007/s10883-012-9136-5

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the Cauchy problem for a general inhomogeneous linear partial differential equation with constant coefficients in two complex variables. We obtain necessary and sufficient conditions for the multisummability of formal solutions in terms of analytic continuation properties and growth estimates of some functions connected with the inhomogeneity. The results are presented in the general framework of 1/p-fractional equations.

引用

页码：103 / 133

页数：31