Geodesic
On the global solubility of the Cauchy problem for hyperbolic Monge--Amp\'ere systems
Izvestiya. Mathematics , Tome 82 (2018) no. 5, pp. 1019-1075.

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This paper is devoted to the global solubility of the Cauchy problem for a class of non-linear hyperbolic systems of two first-order equations with two independent variables. This class contains quasilinear systems. The problem has a unique maximal (with respect to inclusion) many-valued solution, which possesses a completeness property. Namely, characteristics of various families lying on such a solution and converging to the corresponding boundary point have infinite length.
Keywords: non-linear systems, quasilinear systems, Cauchy problem, many-valued solutions, characteristic uniformization. 
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D. V. Tunitsky. On the global solubility of the Cauchy problem for hyperbolic Monge--Amp\'ere systems. Izvestiya. Mathematics , Tome 82 (2018) no. 5, pp. 1019-1075. http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a6/

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