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DOI: 10.46698/t8227-2101-5573-p

Solvability of Cauchy Problem for One System of First Order Quasilinear Differential Equations

Dontsova, M. V.
Vladikavkaz Mathematical Journal 2021. Vol. 23. Issue 3.

Abstract: 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.

Keywords: method of an additional argument, Cauchy problem, first-order partial differential equation

For citation: Dontsova, M. V. Solvability of Cauchy Problem for One System of First Order Quasilinear Differential Equations, Vladikavkaz Math. J., 2021, vol. 23, no. 3, pp. 64-79.
DOI 10.46698/t8227-2101-5573-p

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