Numerical solution of the continuation problem for the one-dimensional acoustics equation

The continuation problem for the acoustics equation is considered in this paper. The continuation problem is reduced to a boundary inverse problem and a generalized solution to the direct problem is given. In the theorem on the existence of a generalized solution of the direct problem, a stability estimate is obtained. For the solution of the inverse problem, the steepest descent method is considered. The gradient of the objective functional is obtained and an algorithm for solving the inverse problem is shown.