Geodesic
The nonlocal solvability conditions for a system of two quasilinear equations of the first order with absolute terms
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 3, pp. 317-328

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The Cauchy problem for a system of two first-order quasilinear equations with absolute terms is considered. The study of this problem's solvability in original coordinates is based on the method of an additional argument. The existence of the local solution of the problem with smoothness which is not lower than the smoothness of the initial conditions, is proved. Sufficient conditions of existence are determined for the nonlocal solution that is continued by a finite number of steps from the local solution. The proof of the nonlocal resolvability of the Cauchy problem relies on original global estimates.
Keywords: method of an additional argument, global estimates, Cauchy problem, first-order partial differential equations. 
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     author = {M. V. Dontsova},
     title = {The nonlocal solvability conditions for a system of two quasilinear equations of the first order with absolute terms},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {317--328},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2019_21_3_a1/}
}
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M. V. Dontsova. The nonlocal solvability conditions for a system of two quasilinear equations of the first order with absolute terms. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 3, pp. 317-328. http://geodesic.mathdoc.fr/item/SVMO_2019_21_3_a1/