Iterative Method for Solving an Inverse Problem for a Hyperbolic Equation with a Small Parameter Multiplying the Highest Derivative

Abstract

We consider the Cauchy problem for a hyperbolic equation with a small parameter multiplying the highest derivative. The inverse problem of finding an unknown function that is a coefficient of the equation and also occurs in the initial condition is posed. The values of the solution of the Cauchy problem and its derivative at x = 0 are given as additional information for solving the inverse problem. An iterative method for determining the unknown function is constructed, and its convergence is proved. Existence theorems are proved for the solution of the inverse problem.