Divergence property of formal solutions for singular first order linear partial differential equations

DOI10.2977/prims/1195143361zbMath0956.35024OpenAlexW1980241662MaRDI QIDQ1577648

Masaki Hibino

Publication date: 7 March 2001

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/1195143361

zbMATH Keywords

Newton polyhedronrate of divergencePoincaré conditionGevrey orderr of formal solutions

Mathematics Subject Classification ID

Series solutions to PDEs (35C10) Cauchy-Kovalevskaya theorems (35A10)

Related Items

Multisummability of formal power series solutions of partial differential equations with constant coefficients ⋮ Solvability of systems of singular partial differential equations in function spaces ⋮ Borel summability of divergent solutions for singularly perturbed first order ordinary differential equations ⋮ Formal Gevrey solutions: in analytic germs -- for higher order holomorphic PDEs ⋮ A Maillet type theorem for first order singular nonlinear partial differential equations ⋮ Singular solutions of nonlinear partial differential equations with resonances ⋮ Asymptotic existence theorems for formal power series whose coefficients satisfy certain partial differential recursions ⋮ Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. I ⋮ Formal Gevrey theory for singular first order quasi-linear partial differential equations ⋮ Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type. II

Cites Work

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• Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations
• On a class of linear partial differential equations whose formal solutions always converge
• A new version of the factorization of a differential equation of the form \(F(x,y,\tau y)=0\)
• Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type. I
• Fredholm property of partial differential operators of irregular singular type
• Newton polygons and gevrey indices for linear partial differential operators
• Convergence of formal solutions of first order singular nonlinear partial differential equations in the complex domain
• On the theorem of Cauchy-Kowalevsky for first order linear differential equations with degenerate principal symbols

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