Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 31, pp. 113.
Exact controllability problem of a wave equation in noncylindrical domains
Hua Wang, Yijun He, Shengjia Li
Abstract:
Let
be a twice continuous differentiable
function which satisfies that
,
is monotone and
for some constants
and
.
The exact controllability of a onedimensional wave equation in a
noncylindrical domain is proved. This equation characterizes small
vibrations of a string with one of its endpoint fixed and the other moving
with speed
.
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
and
.
Submitted December 6, 2014. Published January 30, 2015.
Math Subject Classifications: 35L05, 93B05.
Key Words: Exact controllability; noncylindrical domain;
Hilbert uniqueness method.
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Hua Wang
School of Mathematical Sciences
Shanxi University
Taiyuan 030006, China
email: 197wang@163.com


Yijun He
School of Mathematical Sciences
Shanxi University
Taiyuan 030006, China
email: heyijun@sxu.edu.cn


Shengjia Li
School of Mathematical Sciences
Shanxi University
Taiyuan 030006, China
email: shjiali@sxu.edu.cn

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