The nonlocal solvability conditions in original coordinates for a system with constant terms

Abstract

Conditions of a nonlocal solvability of the Cauchy problem in original coordinates are obtained for a system of two quasilinear first-order  partial differential equations with constant terms. The investigation is based on the method of an additional argument. The proof of the  nonlocal solvability of the Cauchy problem in original coordinates relies on global estimates.