Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity

DOI10.5802/AIF.1867zbMath0993.35003OpenAlexW2519578695MaRDI QIDQ5956581

Zhuangchu Luo, Hidetoshi Tahara, Hua Chen

Publication date: 21 February 2002

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2001__51_6_1599_0

zbMATH Keywords

formal solutionformal Gevrey classGevrey index

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) Series solutions to PDEs (35C10) Cauchy-Kovalevskaya theorems (35A10)

Related Items (14)

Existence and uniqueness theorem for a class of singular nonlinear partial differential equations ⋮ On Gevrey functional solutions of partial differential equations with Fuchsian and irregular singularities ⋮ Unique solvability of second order nonlinear totally characteristic equations ⋮ On \(q\)-asymptotics for linear \(q\)-difference-differential equations with Fuchsian and irregular singularities ⋮ Formal solutions of second order evolution equations ⋮ On the summability of formal solutions for doubly singular nonlinear partial differential equations ⋮ Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations ⋮ On a reduction of nonlinear partial differential equations of Briot-Bouquet type ⋮ On a family of symmetric hypergeometric functions of several variables and their Euler type integral representation ⋮ Singular solutions of nonlinear partial differential equations with resonances ⋮ Unique solvability of some nonlinear partial differential equations with Fuchsian and irregular singularities ⋮ Finitely smooth solutions of nonlinear singular partial differential equations ⋮ Maillet type theorem for nonlinear totally characteristic partial differential equations ⋮ On the summability of the formal solutions for some PDEs with irregular singularity

Cites Work

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• On the holomorphic solution of nonlinear totally characteristic equations with several space variables
• Nonlinear singular first order partial differential equations of Briot- Bouquet type
• Invariant varieties through singularities of holomorphic vector fields
• Holomorphic and singular solutions of nonlinear singular first order partial differential equations
• On totally characteristic type nonlinear partial differential equations in the complex domain
• On the Holomorphic Solution of Non-Linear Totally Characteristic Equations
• Maillet type theorem for nonlinear partial differential equations and Newton polygons

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