Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations

Hidetoshi Tahara, Hiroshi Yamazawa

Research output: Contribution to journalArticle

28 Citations (Scopus)


The paper considers the Cauchy problem for linear partial differential equations of non-Kowalevskian type in the complex domain. It is shown that if the Cauchy data are entire functions of a suitable order, the problem has a formal solution which is multisummable. The precise bound of the admissible order of entire functions is described in terms of the Newton polygon of the equation.

Original languageEnglish
Pages (from-to)3592-3637
Number of pages46
JournalJournal of Differential Equations
Issue number10
Publication statusPublished - 2013 Nov 15



  • Formal solution
  • Linear partial differential equation
  • Multisummability
  • Non-Kowalevskian equation
  • Primary
  • Secondary

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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