Application of Volterra integral equation for inverse problem

Initial value problems for hyperbolic equations with function coefficients are considered in this thesis. It was proved that the solutions of these problems satisfy the 3-D Volterra integral equations with singular kernels. These 3-D Volterra integral equations were solved by the successive approximations. An application of 3-D Volterra integral equation to study one inverse problem for a hyperbolic equation was given. The existence and uniqueness theorems for the solution of an integral equation were proved in the thesis. The result of the thesis generalize and extend Sobolev's result relative to the wave equation with the function velocity.