On the Solvability of a Mixed Problem for an One-dimensional Semilinear Wave Equation with a Nonlinear Boundary Condition

In this paper, for an one-dimensional semilinear wave equation we study a mixed problem with a nonlinear boundary condition. The questions of uniqueness and existence of global and blow-up solutions of this problem are investigated, depending on the nonlinearity nature appearing both in the equation...

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Bibliographic Details
Published in:Journal of contemporary mathematical analysis 2018-09, Vol.53 (5), p.247-259
Main Authors: Kharibegashvili, S. S., Shavlakadze, N. N., Jokhadze, O. M.
Format: Article
Language:English
Subjects:
Boundary conditions
Differential Equations
Mathematics
Mathematics and Statistics
Nonlinearity
Wave equations
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Summary:In this paper, for an one-dimensional semilinear wave equation we study a mixed problem with a nonlinear boundary condition. The questions of uniqueness and existence of global and blow-up solutions of this problem are investigated, depending on the nonlinearity nature appearing both in the equation and in the boundary condition.
ISSN:1068-3623
1934-9416
DOI:10.3103/S1068362318050011