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On the Cauchy problem for quasilinear hyperbolic differential-functional systems in the Schauder canonic form. (English) Zbl 0753.35017
(Author’s abstract.) Classical solutions of quasilinear hyperbolic systems in the Schauder canonic form are investigated. A theorem of existence, uniqueness and continuous dependence on the Cauchy data is proved using the method of bicharacteristics and the Banach fixed-point theorem. The proof of the theorem is based on results due to Cesari and Bassanini for systems without a functional argument [e.g. L. Cesari, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fiz. Mat. Natur. 57(1974), 303-307 (1975; Zbl 0328.35059); Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 1(1974), 311-358 (1975; Zbl 0307.35063); P. Bassanini, Bull. Unione Mat. Ital., V. Ser., A 14, 325-332 (1977; Zbl 0355.35059)].

MSC:
35F25 Initial value problems for nonlinear first-order PDEs
35L60 First-order nonlinear hyperbolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35R10 Functional partial differential equations
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