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Singular nonlinear Cauchy problems. (English) Zbl 0344.35012


MSC:

35F25 Initial value problems for nonlinear first-order PDEs
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
47J05 Equations involving nonlinear operators (general)
35A35 Theoretical approximation in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
35B45 A priori estimates in context of PDEs
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References:

[1] Baouendi, M. S.; Goulaouic, C., Sur une classe de problèmes de Cauchy singuliers non linéaires, C. R. Acad. Sci. Paris, 279, 819-821 (1974) · Zbl 0304.35018
[2] Baouendi, M. S.; Goulaouic, C., Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26, 455-475 (1973) · Zbl 0256.35050
[3] Moser, J., A rapidly convergent iteration method and nonlinear partial differential equations, I, Ann. Scuola Norm. Sup. Pisa, 20, 265-315 (1966) · Zbl 0144.18202
[4] Nagumo, M., Über das Anfangswertproblem Partieller Differentialgleichungen, Japan J. Math., 18, 41-47 (1941) · Zbl 0061.21107
[5] Nirenberg, L., An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Diff. Geom., 6, 561-576 (1972) · Zbl 0257.35001
[6] Ovsjannikov, L. V., Soviet Math., 12, 1497-1502 (1971) · Zbl 0234.35018
[7] Treves, J. F., An abstract nonlinear Cauchy-Kovalevska theorem, Trans. Amer. Math. Soc., 150, 77-92 (1970) · Zbl 0199.15803
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