Newton polygons and gevrey indices for linear partial differential operators

DOI10.1017/S0027763000004207zbMath0815.35007MaRDI QIDQ4039429

Masatake Miyake, Yoshiaki Hashimoto

Publication date: 13 June 1993

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Newton polygonGevrey classesEuler operators

Mathematics Subject Classification ID

Initial value problems for linear higher-order PDEs (35G10) Integro-differential operators (47G20)

Related Items (18)

Multisummability of formal power series solutions of partial differential equations with constant coefficients ⋮ Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations ⋮ On the Borel summability of divergent solutions of the heat equation ⋮ Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space ⋮ Boundary-value problems for fourth-order equations of hyperbolic and composite types ⋮ On \(k\)-summability of formal solutions for a class of partial differential operators with time dependent coefficients ⋮ Gevrey regularity of the solutions of some inhomogeneous semilinear partial differential equations with variable coefficients ⋮ Recent progress in the theory of formal solutions for ODE and PDE. ⋮ On the summability of the solutions of the inhomogeneous heat equation with a power-law nonlinearity and variable coefficients ⋮ Summable solutions of the Goursat problem for some partial differential equations with constant coefficients ⋮ Asymptotic existence theorems for formal power series whose coefficients satisfy certain partial differential recursions ⋮ Formal Gevrey theory for singular first order quasi-linear partial differential equations ⋮ 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 ⋮ Unnamed Item ⋮ Summability of the formal power series solutions of a certain class of inhomogeneous nonlinear partial differential equations with a single level ⋮ Divergence property of formal solutions for singular first order linear partial differential equations ⋮ On the summability of formal solutions of linear partial differential equations

Cites Work

• L'irrégularité en un point singulier d'un système d'équations différentielles linéaires d'ordre 1
• On Cauchy-Kowalevski's theorem for general systems
• Global and local goursat problems in a class of holomorphic or partially holomorphic functions
• Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations
• Newton polygons and formal Gevrey classes

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