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

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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. 
@article{VMJ_2021_23_3_a5,
     author = {M. V. Dontsova},
     title = {Solvability of {Cauchy} problem for one system of first order quasilinear differential equations},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {64--79},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2021_23_3_a5/}
}
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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/