zbMATH — the first resource for mathematics

Nonlinear Fuchs operators. (Opérateurs de Fuchs non linéaires.) (French. English summary) Zbl 1131.35005
Summary: We study in this article nonlinear partial differential equations of Fuchs type in spaces of functions sufficiently differentiable with respect to the Fuchsian variable and in Gevrey spaces with respect the other variables. The results are a generalization of those of Baouendi-Goulaouic obtained in the analytic case.

35C10 Series solutions to PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
Gevrey spaces
Full Text: DOI Numdam EuDML
[1] Baouendi (M.S.), Goulaouic (C).— Cauchy problems with caracteristic initial hypersurface, Comm. on Pure and Appl. Math., 26, p. 455-475 (1973). · Zbl 0256.35050
[2] Baouendi (M.S.), Goulaouic (C.).— Singular Nonlinear Cauchy Problems, J. of Diff. Eq., 22, p. 268-291 (1976). · Zbl 0344.35012
[3] Derrab (F.), Nabaji (A.), Pongérard (P.), Wagschal (C.).— Problème de Cauchy Fuchsien dans les espaces de Gevrey, J. Math. Sci. Univ. Tokyo, 11, p. 401-424 (2004). · Zbl 1064.35039
[4] Koike (M.).— Volevič systems of singular nonlinear partial differential equations, Nonlinear Analysis, Theory, Meth. Appl., 24, p. 999-1009 (1995). · Zbl 0854.35123
[5] Komatsu (H.).— Linear hyperbolic equations with Gevrey coefficients, J. Math. Pures Appl., 59, p. 145-185 (1980). · Zbl 0407.35052
[6] Pongérard (P.).— Sur une classe d’équations de Fuchs non linéaires, J. Math. Sci. Univ. Tokyo, 7, p. 423-448 (2000). · Zbl 0964.35008
[7] Pongérard (P.).— Problème de Cauchy caractéristique à solution entière, J. Math. Sci. Univ. Tokyo, 8, p. 89-105 (2001). · Zbl 0984.35004
[8] Pongérard (P.), Wagschal (C.).— Problème de Cauchy dans des espaces de fonctions entières, J. Math. Pures Appl., 75, p. 409-418 (1996). · Zbl 0858.35001
[9] Tahara (H.).— Cauchy problems for Fuchsian hyperbolic equations in spaces of functions of Gevrey classes, Proc. Japan Acad., 61, p. 63-65 (1985). · Zbl 0586.35060
[10] Tahara (H.).— Singular hyperbolic systems, VI. Asymptotic analysis for Fuchsian hyperbolic equations in Gevrey classes, J. Math. Soc. Japan, 39 No. 4, p. 551-580 (1987). · Zbl 0621.35061
[11] Tahara (H.).— Singular hyperbolic systems, VII. Asymptotic analysis for Fuchsian hyperbolic equations in Gevrey classes (2), Japan. J. Math. New Ser., 15, p. 275-307 (1989). · Zbl 0702.35148
[12] Tahara (H.).— Singular hyperbolic systems, VIII. On the well-posedness in Gevrey classes for Fuchsian hyperbolic equations, J. Fac. Sci. Univ. Tokyo, 39, p. 555-582 (1992). · Zbl 0774.35044
[13] Wagschal(C.).— Le problème de Goursat non linéaire, J. Math. Pures Appl., 58, p. 309-337 (1979). · Zbl 0427.35021
[14] Yamane (H.).— Global fuchsian Cauchy problem, J. Math. Sci. Univ. Tokyo, 7, p. 147-162 (2000). · Zbl 0967.35024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.