Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients

被引：23

作者：

Michalik, Slawomir ^{[1
]}

机构：

[1] Cardinal Stefan Wyszynski Univ, Coll Sci, Fac Math & Nat Sci, PL-01938 Warsaw, Poland

来源：

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2013年 / 56卷 / 01期

关键词：

Linear PDEs with constant coefficients; Formal power series; Moment functions; Moment PDEs; k-summability; Multisummability; POWER-SERIES SOLUTIONS; DIVERGENT SOLUTIONS; FORMAL SOLUTIONS; SUMMABILITY;

D O I：

10.1619/fesi.56.19

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for linear moment partial differential equations with constant coefficients in two complex variables. We construct an integral representation of the solution of this problem and study its analyticity. As a result we derive a characterisation of multisummable formal solutions of the Cauchy problem.

引用

页码：19 / 50

页数：32

共 19 条

[1] Multi summability of formal power series solutions of partial differential equations with constant coefficients [J].

Balser, W .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 201 (01) :63-74

[2] Divergent solutions of the heat equation: On an article of Lutz, Miyake and Schafke [J].

Balser, W .

PACIFIC JOURNAL OF MATHEMATICS, 1999, 188 (01) :53-63

[3]

Balser W., 2005, RECENT TRENDS MICROL, V1412, P151

[4]

Balser W., 2006, ULMER SEMINARE, V11, P29

[5]

Balser W., 1999, ACTA SCI MATH, V65, P543

[6]

BALSER W., 2000, Formal power series and linear systems of meromorphic ordinary differential equations

[7]

Balser W., 2009, Adv. Dyn. Syst. Appl, V4, P159

[8] Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients [J].

Balser, Werner ;

Yoshino, Masafumi .

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2010, 53 (03) :411-434

[9] Integral representation for Borel sum of divergent solution to a certain non-Kowalevski type equation [J].

Ichinobe, K .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2003, 39 (04) :657-693

[10] On the Borel summability of divergent solutions of the heat equation [J].

Lutz, DA ;

Miyake, M ;

Schäfke, R .

NAGOYA MATHEMATICAL JOURNAL, 1999, 154 :1-29

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