Global existence theorems of a solution of the Cauchy problem for systems of the kinetic Carleman and Godunov–Sultangazin equations

We consider the Cauchy problem for the one-dimensional systems of the kinetic Carleman and Godunov–Sultangazin equations with bounded energy and periodic initial data. We present theorems on the global existence of a solution of the Cauchy problem for the Carleman and Godunov–Sultangazin systems.