Generalized mixed problem for the simplest wave equation and its applications

In this paper, we present results for generalized homogeneous and inhomogeneous mixed problems for the wave equation based on the operation of integrating a divergent series of a formal solution using the method of separation of variables. A solution to the generalized mixed problem for an inhomogeneous equation is found under the assumption that the function characterizing the inhomogeneity is locally summable. As an application, a mixed problem with nonzero potential is considered.