Exact controllability for a wave equation with fixed boundary control. (English) Zbl 1304.35395
Summary: This paper addresses the study of the controllability for a one-dimensional wave equation in domains with moving boundary. This equation characterizes the motion of a string with a fixed endpoint and the other one moving. When the speed of the moving endpoint is less than \(1-\frac{2}{1+e^2}\), by the Hilbert Uniqueness Method, the exact controllability of this equation is established. Also, the explicit dependence of the controllability time on the speed of the moving endpoint is given.
MSC:
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 93B05 | Controllability |
| 74K05 | Strings |
References:
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