Abstract
A system of two Kirchhoff plate equations with nonlinear coupling through both the boundary and the interior is considered. For this problem, it is proven that by appropriately choosing feedback controls, the energy of the system decays at a uniform rate. This result extends previous results in a number of directions: (i) it does not require any geometric hypotheses to be imposed on the domain; (ii) it allows for the presence of nonlinear coupling terms; (iii) it does not require the control functions to satisfy any growth conditions at the origin.
This material is based upon work partially supported under a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship.
Partially supported by National Science Foundation Grant NSF DMS-9204338.
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© 1994 Springer Basel AG
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Horn, M.A., Lasiecka, I. (1994). Uniform Stabilizability of Nonlinearly Coupled Kirchhoff Plate Equations. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena. ISNM International Series of Numerical Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8530-0_11
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DOI: https://doi.org/10.1007/978-3-0348-8530-0_11
Publisher Name: Birkhäuser, Basel
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