Global existence and uniqueness of a classical solution to some differential evolutionary system

Abstract

Theorems of global existence and uniqueness of a classical solution to a nonlinear differential evolutionary system with initial conditions are proved. This system is composed of one partial hyperbolic second-order equation and an ordinary subsystem with a parameter. In the proof of the theorems we use the Picard iteration method, the monotone method of lower and upper solutions, the integral form of the differential problem, weak differential inequalities and the Arzeli-Ascola lemma.