Geodesic
Global and blowup solutions of a~mixed problem with nonlinear boundary conditions for a~one-dimensional semilinear wave equation
Sbornik. Mathematics, Tome 205 (2014) no. 4, pp. 573-599

Voir la notice de l'article provenant de la source Math-Net.Ru

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles.
Keywords: semilinear wave equation, nonlinear boundary conditions, a priori estimate, comparison theorems, global and blowup solutions. 
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     title = {Global and blowup solutions of a~mixed problem with nonlinear boundary conditions for a~one-dimensional semilinear wave equation},
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S. S. Kharibegashvili; O. M. Jokhadze. Global and blowup solutions of a~mixed problem with nonlinear boundary conditions for a~one-dimensional semilinear wave equation. Sbornik. Mathematics, Tome 205 (2014) no. 4, pp. 573-599. http://geodesic.mathdoc.fr/item/SM_2014_205_4_a5/