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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_2018_82_5_a6,
     author = {D. V. Tunitsky},
     title = {On the global solubility of the {Cauchy} problem for hyperbolic {Monge--Amp\'ere} systems},
     journal = {Izvestiya. Mathematics },
     pages = {1019--1075},
     publisher = {mathdoc},
     volume = {82},
     number = {5},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a6/}
}
TY  - JOUR
AU  - D. V. Tunitsky
TI  - On the global solubility of the Cauchy problem for hyperbolic Monge--Amp\'ere systems
JO  - Izvestiya. Mathematics 
PY  - 2018
SP  - 1019
EP  - 1075
VL  - 82
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a6/
LA  - en
ID  - IM2_2018_82_5_a6
ER  - 
%0 Journal Article
%A D. V. Tunitsky
%T On the global solubility of the Cauchy problem for hyperbolic Monge--Amp\'ere systems
%J Izvestiya. Mathematics 
%D 2018
%P 1019-1075
%V 82
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a6/
%G en
%F IM2_2018_82_5_a6
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/