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.

中文翻译：

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一维半线性波动方程非线性边界条件混合问题的可解性

对于一维半线性波动方程，考虑非线性边界条件的混合问题。根据方程和边界条件中的非线性类型，研究所考虑问题的唯一性以及局部和全局可解性。不仅考虑全局而且甚至局部不存在解决方案的情况，以及该问题具有爆炸解决方案的情况。