Geodesic
Sufficient conditions of a nonlocal solvability for a system of two quasilinear equations of the first order with constant terms
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 55 (2020), pp. 60-78

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We consider a Cauchy problem for a system of two quasilinear equations of the first order with constant terms. The study of the solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms in the original coordinates is based on the method of an additional argument. Theorems on the local and nonlocal existence and uniqueness of solutions to the Cauchy problem are formulated and proved. We prove the existence and uniqueness of the local solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms, which has the same smoothness with respect to $x$ as the initial functions of the Cauchy problem. Sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms are found; this solution is continued by a finite number of steps from the local solution. The proof of the nonlocal solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms relies on global estimates.
Keywords: a system of quasilinear equations, the method of an additional argument, Cauchy problem, global estimates. 
@article{IIMI_2020_55_a4,
     author = {M. V. Dontsova},
     title = {Sufficient conditions of a nonlocal  solvability  for  a  system of two quasilinear equations of the first order  with   constant terms},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {60--78},
     publisher = {mathdoc},
     volume = {55},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2020_55_a4/}
}
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M. V. Dontsova. Sufficient conditions of a nonlocal  solvability  for  a  system of two quasilinear equations of the first order  with   constant terms. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 55 (2020), pp. 60-78. http://geodesic.mathdoc.fr/item/IIMI_2020_55_a4/