Geodesic
Solvability of a Mixed Problem with Nonlinear Boundary Condition for a One-Dimensional Semilinear Wave Equation
Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 137-152

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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.
Keywords: semilinear wave equation, nonlinear boundary condition, a priori estimate, local and global solvability, nonexistence of a solution, blow-up solutions. 
@article{MZM_2020_108_1_a10,
     author = {S. S. Kharibegashvili and O. M. Dzhokhadze},
     title = {Solvability of a {Mixed} {Problem} with {Nonlinear} {Boundary} {Condition} for a {One-Dimensional} {Semilinear} {Wave} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {137--152},
     publisher = {mathdoc},
     volume = {108},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_1_a10/}
}
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S. S. Kharibegashvili; O. M. Dzhokhadze. Solvability of a Mixed Problem with Nonlinear Boundary Condition for a One-Dimensional Semilinear Wave Equation. Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 137-152. http://geodesic.mathdoc.fr/item/MZM_2020_108_1_a10/