TO THE QUESTION OF A MULTIPOINT MIXED BOUNDARY VALUE PROBLEM FOR A WAVE EQUATION

Abstract

It is well known that some problems in mechanics and physics lead to partial differential equations of the hyperbolic type. A classical example of the hyperbolic type is wave equation. When posed, the task sometimes lacks the classical boundary condition and the need arises to have a nonlocal boundary condition. Aim our work is get D'Alembert formula for mixed boundary value problem generated by a wave equation. In the classical case, given D'Alembert formula for boundary value problem generated by a wave equation. In our case, we must give D'Alembert formula for mixed boundary value problem. For this, we consider ordinary differential operator L withnon-local boundary conditions. We search the solution of the wave equation like a sum with eigenfunction of the operator L. There are we use that fact, that eigenfunction of the operator L is Riesz basis in L-2 (0, l). Through this method and calculation we get D'Alembert formula.