Four mixed problems for the vibrating string equation with boundary and nonlocal Dirichlet and Neumann conditions

Four mixed problems for the vibrating string equation with boundary and nonlocal dirichlet and neumann conditions has been demonstrated. Weak solutions of the wave equation for the four mixed problems with zero initial conditions, the boundary condition, and the nonlocal condition with an arbitrary constant are provided. The weak solution in the class of the mixed problem for wave equation with zero initial conditions and one of the collections of the boundary and nonlocal conditions is a function that satisfies the integral identity.