Abstract:
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.
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