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 variablesis considered. By introducing additional functional parameters, we investigate the solvability of the problem and developan algorithm for finding its approximate solutions. The problem is reduced to an equivalent one, consisting of theGoursat problem for a hyperbolic equation with parameters and boundary value problems with an integral conditionfor ODEs with respect to the parameters entered. We propose an algorithm to find an approximate solution to theoriginal problem, which is based on the algorithm for finding a solution to the equivalent problem. The convergenceof the algorithms is proved. A coefficient criterion for the unique solvability of the integral-boundary value problem isestablished.