On the existence and uniqueness of a generalized solution of the mixed problem for the wave equation with the second and third boundary conditions

被引:0
|
作者
A. A. Nikitin
机构
[1] Moscow State University,
来源
Differential Equations | 2013年 / 49卷
关键词
Wave Equation; Generalize Solution; Boundary Control; Mixed Problem; Integral Identity;
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摘要
We prove the uniqueness of a generalized solution of an initial-boundary value problem for the wave equation with boundary conditions of the third and second kind. In addition, we find a closed-form expression for the analytic solution of that problem with zero initial data. The result plays an important role in the investigation of the boundary control problem. We show how to use the obtained solution for the investigation of the boundary control problem in the case of subcritical time intervals for which the solution of the boundary control problem, if it exists at all, is unique. We obtain necessary and sufficient conditions for the existence of a unique solution in a class admitting the existence of finite energy.
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页码:645 / 653
页数:8
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