Geodesic
Solvability of Cauchy problem for one system of first order quasilinear differential equations
Vladikavkazskij matematičeskij žurnal, Tome 23 (2021) no. 3, pp. 64-79 
M. V. Dontsova. Solvability of Cauchy problem for one system of first order quasilinear differential equations. Vladikavkazskij matematičeskij žurnal, Tome 23 (2021) no. 3, pp. 64-79. http://geodesic.mathdoc.fr/item/VMJ_2021_23_3_a5/
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     author = {M. V. Dontsova},
     title = {Solvability of {Cauchy} problem for one system of first order quasilinear differential equations},
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     url = {http://geodesic.mathdoc.fr/item/VMJ_2021_23_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the Cauchy problem for a system of first-order quasilinear differential equations. The solvability of the problem is investigated in the initial coordinates using the additional argument method. Sufficient conditions for the existence and uniqueness of a local solution which has the same smoothness in the independent variable as the initial functions of the Cauchy problem are determined. An existence and uniqueness theorem of a local solution is proved. Sufficient conditions for the existence and uniqueness of a global solution are determined. The proof of the global solvability relies upon global estimates.

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