TY - JOUR
T1 - Global smooth solutions and exponential stability for a nonlinear beam
AU - Yao, Peng Fei
AU - Weiss, George
PY - 2007
Y1 - 2007
N2 - In this paper we consider a dynamical system with boundary input and output describing the bending vibrations of a quasi-linear beam, where the nonlinearity comes from Hooke's law. First we derive an existence result for short-time solutions of the system of equations. Then we show that the structure of the boundary input and output forces the system to admit global solutions at least when the initial data and the boundary input are small in a certain sense. In particular, we prove that the norm of the state of the system decays exponentially if the input becomes zero after a finite time (the input being zero can be understood as a boundary feedback).
AB - In this paper we consider a dynamical system with boundary input and output describing the bending vibrations of a quasi-linear beam, where the nonlinearity comes from Hooke's law. First we derive an existence result for short-time solutions of the system of equations. Then we show that the structure of the boundary input and output forces the system to admit global solutions at least when the initial data and the boundary input are small in a certain sense. In particular, we prove that the norm of the state of the system decays exponentially if the input becomes zero after a finite time (the input being zero can be understood as a boundary feedback).
KW - Boundary input and output
KW - Energy-preserving system
KW - Exponential stabilization
KW - Quasi-linear beam
UR - http://www.scopus.com/inward/record.url?scp=34548140257&partnerID=8YFLogxK
U2 - 10.1137/S0363012903435357
DO - 10.1137/S0363012903435357
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AN - SCOPUS:34548140257
SN - 0363-0129
VL - 45
SP - 1931
EP - 1964
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
IS - 6
ER -