Uniform Stabilization of a Thin Cylindrical Shell with Rotational Inertia Terms
We consider a well-known model of a thin cylindrical shell with rotational inertia terms. We introduce suitable dissipative feedback controls on the boundary in the form of forces, shears, and moments and show that the resulting closed loop feedback problem generates a s.c. semigroup of contractions in the energy space and that the corresponding energy of the system decays exponentially in the uniform topology. Consequently, we obtain the exact controllability of the cylinder by explicit boundary controls.
KeywordsBilinear Form Unique Continuation Neutral Surface Exact Controllability Uniform Stabilization
Unable to display preview. Download preview PDF.
- Bernadou, M. “Methodes d’elements finis pour les problemes de coques minces,” in Reserches en mathematiques appliquees,P.G. Ciarlet and J.L. Lions, eds., Masson, Paris.Google Scholar
- Bradley, M. and McMillan, C., “Well-posedness of a nonlinear spherical cap,” to appear in Nonlinear Analysis. Google Scholar
- Horn, M.A. and Lasiecka, I. (1994),“Global stabilization of a dynamic von Karman plate with nonlinear boundary feedback,” Applied Mathematics and Optimization. Google Scholar
- Lasiecka, I., Triggiani, R. and Valente, W. (1995),“Exponential decay rates for spherical caps with boundary dissipation,” preprint.Google Scholar
- Lasiecka, I. and Valente, W. (1995),“Uniform boundary stabilization of a nonlinear shallow and thin elastic spherical cap,” preprint.Google Scholar
- Lions, J.L. (1988), Controlabilite exacte, perturbation et stabilization des systems distributes, Vol. 1,Masson, Paris.Google Scholar
- McMillan, C. (1996), Uniform stabilization of a thin cylindrical shell,preprint.Google Scholar
- Taylor, M. (1981), Pseudodifferential Operators,Princeton University Press, Princeton, New Jersey.Google Scholar