On the global solubility of the Monge--Ampere hyperbolic equations

D. V. Tunitsky

Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 1069-1111.

Résumé

This paper is devoted to the solubility of the Cauchy problem for the Monge–Ampere hyperbolic equations, in particular, for quasi-linear equations with two independent variables. It is proved that this problem has a unique maximal solution in the class of multi-valued solutions. The notion of a multi-valued solution goes back to Monge, Lie, et al. It is an historical predecessor of the notion of a generalized solution in the Sobolev–Schwartz sense. The relationship between multi-valued and generalized solutions of linear differential equations is established.

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