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

Аннотация

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
withnon–local boundary conditions. We search the solution of the wave equation like a sum with eigenfunction of
the operator . There are we use that fact, that eigenfunction of the operator is Riesz basis in 0,. Through
this method and calculation we get D’Alembert formula.