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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; Ovsjannikov, L.V, A nonlinear Cauchy problem in a scale of Banach spaces, Dokl. akad. nauk SSSR, Soviet math., 12, No. 4, 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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