Electron. J. Diff. Equ.,
Vol. 2016 (2016), No. 216, pp. 117.
Wellposedness and exact controllability of a fourth order Schrodinger
equation with variable coefficients and Neumann boundary control
and collocated observation
Ruili Wen, Shugen Chai
Abstract:
We consider an openloop system of a fourth order Schrodinger equation
with variable coefficients and Neumann boundary control and collocated
observation. Using the multiplier method on Riemannian manifold we show that
that the system is wellposed in the sense of Salamon.
This implies that the exponential stability of the closedloop system under
the direct proportional output feedback control and the exact controllability
of openloop system are equivalent. So in order to conclude feedback
stabilization from wellposedness, we study the exact controllability under
a uniqueness assumption by presenting the observability inequality for the
dual system. In addition, we show that the system is regular in the sense
of Weiss, and that the feedthrough operator is zero.
Submitted May 25, 2016. Published August 12, 2016.
Math Subject Classifications: 93C20, 35L35, 35B37.
Key Words: Fourth order Schrodinger equation; variable coefficients;
wellposedness; exact controllability; boundary control;
boundary observation.
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Ruili Wen
School of Mathematical Sciences
Shanxi University, Taiyuan 030006, China
email: wenruili@sxu.edu.cn


Shugen Chai
School of Mathematical Sciences
Shanxi University, Taiyuan 030006, China
email: sgchai@sxu.edu.cn

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