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.
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