The classical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

In this article, we study the classical solution of mixed problem in a quarter plane for one-dimensional wave equation. On bottom boundary, Cauchy conditions are specified, and second them has discontinuity first kind at point. The smooth boundary condition is set side boundary. built using method characteristics an explicit analytical form. uniqueness proved, under which piecewise-smooth exists established. with conjugate considered