Solvability of a Mixed Problem with Nonlinear Boundary Condition for a One-Dimensional Semilinear Wave Equation

For a one-dimensional semilinear wave equation, a mixed problem with nonlinear boundary condition is considered. The uniqueness and the local and global solvability of the problem under consideration are studied depending on the type of nonlinearities in the equation and in the boundary conditions. The cases of nonexistence of a solution not only globally but even locally are considered, as well as the case where this problem has a blow-up solution.