Numerical Calculations Models for Physical-Mechanical Systems

On One Nonlocal Boundary Value Problem For The Inverse Hyperbolic Equation Of Second Order

Ya. T. Megraliev

Department of Differential and Integral Equations of Baku State University.

Abstract: In this work an inverse problem for the hyperbolic equation of second order with periodical boundary conditions is investigated. At first given problem is reduced to the equivalent problem in a known sense. Then, using the Fourier method equivalent problem is reduced to the solution of the system of integral equations. Further, the existence and uniqueness of the integral equation is proved by means of the contraction mappings principle, which is also the unique solution of the equivalent problem. Finally, using the equivalence, the theorem on the existence and uniqueness of a classical solution of the given problem is proved.

Keywords: Inverse boundary problem, hyperbolic equation, Fourier method, classic solution.

UDC: 517.95

Received: 08.01.2013
Revised: 01.07.2013