An integral-boundary value problem for a partial differential equation of second order

Abstract

An integral-boundary value problem for a hyperbolic partial differential equation in two independent variables is considered. By introducing additional functional parameters, we investigate the solvability of the problem and develop an algorithm for finding its approximate solutions. The problem is reduced to an equivalent one, consisting of the Goursat problem for a hyperbolic equation with parameters and boundary value problems with an integral condition for ODEs with respect to the parameters entered. We propose an algorithm to find an approximate solution to the original problem, which is based on the algorithm for finding a solution to the equivalent problem. The convergence of the algorithms is proved. A coefficient criterion for the unique solvability of the integral-boundary value problem is established.