A generalized integral problem for a system of hyperbolic equations and its applications

Abstract

A nonlocal boundary value problem for a system of hyperbolic equations of second order with generalized integral condition is considered. By method of introduction of functional parameters the investigated problem is transformed to the inverse problem for the system of hyperbolic equations with unknown parameters and additional functional relations. Algorithms of finding solution to the inverse problem for the system of hyperbolic equations are constructed, and their convergence is proved. The conditions for existence of unique solution to the inverse problem for the system of hyperbolic equations are obtained in the terms of initial data. The coefficient conditions for unique solvability of nonlocal boundary value problem for the system of hyperbolic equations with generalized integral condition are established. The results are illustrated by numerical examples.

Keywords

• hyperbolic equation
• inverse nonlocal problem
• generalized integral condition
• algorithm
• solvability

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