Weak approximation method for the Cauchy problem for a one-dimensional system of Hopf-type equations

A system of Hopf-type equations is obtained. The Cauchy problem for a one-dimensional system of equations of the Hopf type which arises in two-velocity hydrodynamics is considered. The existence and uniqueness of a solution to the Cauchy problem for the one-dimensional system of the Hopf type is proved by the method of weak approximation.