Integral representation for Borel sum of divergent solution to a certain non-Kowalevski type equation

DOI10.2977/prims/1145476043zbMath1063.35049OpenAlexW1997738276MaRDI QIDQ1884460

Kunio Ichinobe

Publication date: 1 November 2004

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1145476043

zbMATH Keywords

Borel summabilityNon-Kowalevski type equationpower series solution.

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Series solutions to PDEs (35C10) Asymptotic expansions of solutions to PDEs (35C20) Cauchy-Kovalevskaya theorems (35A10) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Related Items (11)

Summability of divergent solutions of the \(n\)-dimensional heat equation ⋮ Summability and fractional linear partial differential equations ⋮ Decomposition of solutions of the Cauchy problem of a quasi-homogeneous partial differential equation ⋮ Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients ⋮ Summable solutions of the Goursat problem for some partial differential equations with constant coefficients ⋮ The Mathematics of Superoscillations ⋮ Summability of formal solutions of linear partial differential equations with divergent initial data ⋮ The Borel summable solutions of heat operators on a real analytic manifold ⋮ On the multisummability of divergent solutions of linear partial differential equations with constant coefficients ⋮ The Stokes phenomenon for certain partial differential equations with meromorphic initial data ⋮ On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations

Cites Work

• Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations
• A remark on Cauchy-Kowalevski's theorem
• Divergent solutions of the heat equation: On an article of Lutz, Miyake and Schäfke
• From divergent power series to analytic functions. Theory and application of multisummable power series
• Generalized hypergeometric functions with applications in statistics and physical sciences
• The special functions and their approximations. Vol. I, II
• On the Borel summability of divergent solutions of the heat equation
• The Borel sum of divergent Barnes hypergeometric series and its application to a partial differential equation
• Maillet type theorem for nonlinear partial differential equations and Newton polygons
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