EXACT CONTROLLABILITY PROBLEM OF A WAVE EQUATION IN NON-CYLINDRICAL DOMAINS

被引:0
作者
Wang, Hua [1 ]
He, Yijun [1 ]
Li, Shengjia [1 ]
机构
[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China
关键词
Exact controllability; non-cylindrical domain; Hilbert uniqueness method;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let alpha : [0, infinity) > (0, infinity) be a twice continuous differentiable function which satisfies that alpha(0) = 1, alpha' is monotone and 0 < c(1) <= alpha'(t) (t) <= c(2) < 1 for some constants c(1), c(2). The exact controllability of a one-dimensional wave equation in a non-cylindrical domain is proved. This equation characterizes small vibrations of a string with one of its endpoint fixed and the other moving with speed alpha'(t). By using the Hilbert Uniqueness Method, we obtain the exact controllability results of this equation with Dirichlet boundary control on one endpoint. We also give an estimate on the controllability time that depends only on c(1) and c(2).
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页数:13
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