On the boundary conditions of the wave potential in a domain with a curviline borders

We study a one-dimensional volume wave potential in a domain with curvilinear boundaries. As a kernel of the wave potential we have chosen the fundamental solution of the Cauchy problem. It is well-known that in this case the volume wave potential satisfies one-dimensional initial conditions of Cauchy. We have constructed boundary conditions to which the wave potential satisfies at lateral boundaries of the domain. It is shown that the formulated initial-boundary value problem has the unique classical solution.