Formal Gevrey theory for singular first order quasi-linear partial differential equations

DOI10.2977/prims/1166642193zbMath1120.35031OpenAlexW1965355240MaRDI QIDQ998132

Masaki Hibino

Publication date: 10 August 2007

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

Full work available at URL: https://projecteuclid.org/euclid.prims/1166642193

zbMATH Keywords

convergenceexistenceuniquenessNewton polyhedronrate of divergenceformal power series solutionGevrey theorysingular PDE

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Series solutions to PDEs (35C10) Cauchy-Kovalevskaya theorems (35A10)

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
• Formal Gevrey theory for singular first order semi-linear partial differential equations
• Divergence property of formal solutions for singular first order linear partial differential equations
• Formal power series solutions in a parameter
• 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
• Formal Gevrey class of formal power series solution for singular first order linear partial differential operators

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