Open Access
1996 Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan-Taylor damping
Yuncheng You
Abstr. Appl. Anal. 1(1): 83-102 (1996). DOI: 10.1155/S1085337596000048


In this paper we study a hinged, extensible, and elastic nonlinear beam equation with structural damping and Balakrishnan-Taylor damping with the full exponent 2(n+β)+1. This strongly nonlinear equation, initially proposed by Balakrishnan and Taylor in 1989, is a very general and useful model for large aerospace structures. In this work, the existence of global solutions and the existence of absorbing sets in the energy space are proved. For this equation, the feature is that the exponential rate of the absorbing property is not a global constant, but which is uniform for the family of trajectories starting from any given bounded set in the state space. Then it is proved that there exists an inertial manifold whose exponentially attracting rate is accordingly non-uniform. Finally, the spillover problem with respect to the stabilization of this equation is solved by constructing a linear state feedback control involving only finitely many modes. The obtained results are robust in regard to the uncertainty of the structural parameters.


Download Citation

Yuncheng You. "Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan-Taylor damping." Abstr. Appl. Anal. 1 (1) 83 - 102, 1996.


Published: 1996
First available in Project Euclid: 7 April 2003

zbMATH: 0940.35036
MathSciNet: MR1390561
Digital Object Identifier: 10.1155/S1085337596000048

Primary: 35B40 , 35L75
Secondary: 73K05 , 93D15

Keywords: Balakrishnan-Taylor damping , dissipative solution semigroup , Inertial manifold , nonlinear beam equation , stabilization

Rights: Copyright © 1996 Hindawi

Vol.1 • No. 1 • 1996
Back to Top