Solvability in the class of multivalued solutions is investigated for Cauchy problems for hyperbolic Monge-Ampère equations. A characteristic uniformization is constructed on definite solutions of this problem, using which the existence and uniqueness of a maximal solution is established. It is shown that the characteristics in the different families that lie on a maximal solution and converge to a definite boundary point have infinite lengths. In this way a theory of global solvability is developed for the Cauchy problem for hyperbolic Monge-Ampère equations, which is analogous to the corresponding theory for ordinary differential equations. Using the same methods, a stable explicit difference scheme for approximating multivalued solutions can be constructed and a number of problems which are important for applications can be integrated by quadratures. Bibliography: 23 titles.

中文翻译：

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双曲Monge-Ampère方程的多值解：可解性，可积性，逼近

针对双曲Monge-Ampère方程的Cauchy问题，研究了多值解类的可解性。在此问题的确定解上构造特征均匀性，由此建立最大解的存在性和唯一性。结果表明，位于最大解上并收敛到确定边界点的不同族的特征具有无限的长度。通过这种方式，为双曲Monge-Ampère方程的Cauchy问题开发了一个整体可解性理论，该理论类似于常微分方程的相应理论。使用相同的方法 可以构造用于逼近多值解的稳定的显式差分方案，并且可以通过求积分来集成许多对应用重要的问题。参考书目：23种。