Analytic and Summable Solutions of Inhomogeneous Moment Partial Differential Equations

被引:9
作者
Michalik, Slawomir [1 ]
机构
[1] Cardinal Stefan Wyszynski Univ, Fac Math & Nat Sci, Coll Sci, Woycickiego 1-3, PL-01938 Warsaw, Poland
来源
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2017年 / 60卷 / 03期
关键词
Linear PDEs with constant coefficients; Formal power series; Moment functions; Moment-PDEs; Gevrey order; Borel summability; Multisummability; FORMAL POWER-SERIES; SUMMABILITY;
D O I
10.1619/fesi.60.325
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the Cauchy problem for a general inhomogeneous linear moment partial differential equation of two complex variables with constant coefficients, where the inhomogeneity is given by the formal power series. We state sufficient conditions for the convergence, analytic continuation and summability of formal power series solutions in terms of properties of the inhomogeneity. We consider both the summability in one variable t (with coefficients belonging to some Banach space of Gevrey series with respect to the second variable z) and the summability in two variables (t, z).
引用
收藏
页码:325 / 351
页数:27
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