Abstract:
The subject of the paper is the solubility of the Cauchy problem for strictly hyperbolic
systems of Monge–Ampère equations and, in particular, for
quasilinear systems of equations with two independent variables. It
is proved that this problem has a unique maximal solution in the
class of immersed many-valued solutions. Maximal many-valued
solutions have the following characteristic property of
completeness: either the characteristics of distinct families
starting at two fixed points in the initial curve in the compatible
directions intersect or the lengths of the characteristics in
either family starting in the same direction from the interval of
the initial curve connecting the fixed points make up an unbounded
set. The completeness property is an analogue of the property that a
non-extendable integral curve of an ordinary differential
equation approaches the boundary of the definition domain of the
equation.
Bibliography: 19 titles.
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