Generalized solutions in \(L_2\) of the second boundary value problem for the wave equation (Q2387925)

The article refers to boundary value problems with initial or terminal conditions for the wave equation. The boundary conditions involve values of the first order partial derivative of the solution with respect to space variable at the boundary of the interval \([0,L]\). The notion of antiderivative of a distribution is defined. For both, initial and terminal condition problems, one shows the uniqueness of a generalized solution. In case zero initial or terminal conditions, the generalized solutions are expressed as linear combinations of antiderivatives of functions in the right side of boundary conditions. A priori estimates for solutions are proved.