INVERSE PROBLEM FOR ONE SYSTEM OF HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATIONS OF FIRST ORDER

Abstract

The one-dimensional system of hyperbolic integro-differential equations with convolution integral on the right side is considered. The direct problem is represented by the Cauchy problem for this equation. In this paper it is  studied the inverse problem consisting in finding kernel of the integrated members on known at the point x=x0  for t>0  to the solution of direct problem. This problem is replaced with the equivalent system of integral equations with respect to unknown functions and on the bases of coutractive mapping principle it is proved the unique solvability to the direct and inverse problems.