On sufficient conditions for convergence of formal solutions
Copyright policy )On sufficient conditions for convergence of formal solutions
L'auteur donne des conditions suffisantes de convergence de solutions formelles d'équations aux dérivées partielles dans \(C^ 2\) obtenues comme polynômes à coefficient analytiques des champs de vecteurs \((x_ 1 \partial_{x_ 1})\) et \((x_ 2 \partial_{x_ 2})\) vérifiant des conditions du type de Fuchs. Il généralise ainsi des résultats de \textit{M. Kashiwara, T. Kawai} et \textit{J. Sjöstrand} [Ark. Mat. 17, 83-91 (1979; Zbl 0411.35003)].
35A20, 35C10, convergence, Siegel condition, Linear higher-order PDEs, convergence of formal solutions, diophantine function, formal solutions, Series solutions to PDEs, Analyticity in context of PDEs, analytic Fuchsian equations
35A20, 35C10, convergence, Siegel condition, Linear higher-order PDEs, convergence of formal solutions, diophantine function, formal solutions, Series solutions to PDEs, Analyticity in context of PDEs, analytic Fuchsian equations
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