Electron. J. Diff. Equ., Vol. 2015 (2015), No. 239, pp. 1-19.

Boundary controllability for a nonlinear beam equation

Xiao-Min Cao

This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L)$ and with control functions in $H^2(0,T)$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.

Submitted May 4, 2015. Published September 17, 2015.
Math Subject Classifications: 93B05, 35L75, 93C10, 93C20.
Key Words: Nonlinear beam equation; locally exact controllability; equilibrium; smooth control.

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Xiao-Min Cao
School of Mathematical Sciences
Shanxi University
Taiyuan 030006, China
email: caoxm@sxu.edu.cn

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