Geodesic
Exact controllability problem of a wave equation in non-cylindrical domains
Electronic journal of differential equations, Tome 2015 (2015)
Let $\alpha: [0, \infty)\to(0, \infty)$ be a twice continuous differentiable function which satisfies that $\alpha(0)=1, \alpha'$ is monotone and $0$ for some constants $c_1$ and $c_2$. 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 $c_2$.
Classification : 35L05, 93B05
Keywords: exact controllability, non-cylindrical domain, Hilbert uniqueness method 
@article{EJDE_2015__2015__a11,
     author = {Wang,  Hua and He,  Yijun and Li,  Shengjia},
     title = {Exact controllability problem of a wave equation in non-cylindrical domains},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1315.35118},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a11/}
}
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VL  - 2015
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%A He,  Yijun
%A Li,  Shengjia
%T Exact controllability problem of a wave equation in non-cylindrical domains
%J Electronic journal of differential equations
%D 2015
%V 2015
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a11/
%G en
%F EJDE_2015__2015__a11
Wang,  Hua; He,  Yijun; Li,  Shengjia. Exact controllability problem of a wave equation in non-cylindrical domains. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a11/