Periodic solutions of boundary value problems for hyperbolic equations with a mixed derivative

Abstract

The monograph is devoted to the study of periodic boundary value problems for systems of hyperbolic equations with a mixed derivative. The work proposes methods for finding approximate solutions of periodic boundary value problems for systems of linear hyperbolic equations. The coefficient characteristics of the unique solvability of the periodic boundary value problem for a system of linear hyperbolic equations are established. The definition of the isolated solution of a semi-periodic boundary value problem for the nonlinear system of the hyperbolic equations, generalizing definition of the isolated solution of nonlinear boundary value problems for ordinary differential equations are introduced. The criterion for the existence of a solution of a semi-periodic boundary value problem for systems of nonlinear hyperbolic equations in terms of the problem data is established. The main theorems of the work are illustrated by examples. The monograph is of interest to teachers, undergraduates and university students.