Summability of formal solutions of linear partial differential equations with divergent initial data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:406

Article

Michalik, Slawomir^1,2 

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

[2] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

关键词: Linear PDEs with constant coefficients;    Formal power series;    Moment functions;    Moment-PDEs;    Gevrey order;    Borel summability;    Multisummability;   

DOI  :  10.1016/j.jmaa.2013.04.062

来源: Elsevier

【 摘 要 】

We study the Cauchy problem for a general homogeneous linear partial differential equation in two complex variables with constant coefficients and with divergent initial data. We state necessary and sufficient conditions for the summability of formal power series solutions in terms of properties of divergent Cauchy data. 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). The results are presented in the general framework of moment-PDEs. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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