Nonlocal solvability conditions for Cauchy problem for a system of first order partial differential equations with special right-hand sides

We consider a Cauchy problem for a system of two quasilinear first order partial differential equations with special right-hand sides. We obtain the conditions of a nonlocal solvability of this Cauchy problem. The study of the nonlocal solvability of the Cauchy problem for a system of two quasilinear differential equations with special right-hand sides is based on the method of an additional argument. The proof of the nonlocal resolvability of the Cauchy problem for a system of two quasilinear first order partial differential equations with special right-hand sides relies on global estimates.