Summability of divergent solutions of the \(n\)-dimensional heat equation

DOI10.1016/j.jde.2006.06.005zbMath1105.35025OpenAlexW1979584190MaRDI QIDQ855813

Sławomir Michalik

Publication date: 7 December 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.06.005

zbMATH Keywords

formal solutionBorel summabilitymodified Borel transform

Mathematics Subject Classification ID

Heat equation (35K05) Series solutions to PDEs (35C10) Initial value problems for second-order parabolic equations (35K15)

Related Items (13)

Summability and fractional linear partial differential equations ⋮ Gevrey regularity of the solutions of some inhomogeneous semilinear partial differential equations with variable coefficients ⋮ Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients ⋮ On the summability of the solutions of the inhomogeneous heat equation with a power-law nonlinearity and variable coefficients ⋮ Mean-value properties of real analytic functions ⋮ Summability of formal solutions to the \(n\)-dimensional inhomogeneous heat equation ⋮ Formal solutions of semilinear heat equations ⋮ 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 ⋮ Gevrey properties and summability of formal power series solutions of some inhomogeneous linear Cauchy-Goursat problems ⋮ Gevrey index theorem for the inhomogeneous n-dimensional heat equation with a power-law nonlinearity and variable coefficients ⋮ Summability of the formal power series solutions of a certain class of inhomogeneous nonlinear partial differential equations with a single level

Cites Work

• Multisummability of formal power series solutions of nonlinear meromorphic differential equations
• Divergent solutions of the heat equation: On an article of Lutz, Miyake and Schäfke
• Multisummability of formal solutions of some linear partial differential equations
• Multisummability of formal power series solutions of partial differential equations with constant coefficients
• Integral representation for Borel sum of divergent solution to a certain non-Kowalevski type equation
• Summability of divergent series
• Formal power series and linear systems of meromorphic ordinary differential equations
• 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
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