This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length . 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 and with control functions in . 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.
Show me the PDF file (277 KB), TEX file, and other files for this article.
| Xiao-Min Cao |
School of Mathematical Sciences
Taiyuan 030006, China
Return to the EJDE web page