ON BOUNDARY CONTROLLABILITY OF A VIBRATING PLATE

Journal article


Publication Details

Author(s): Leugering G, Krabs W, Seidman TI
Journal: Applied Mathematics and Optimization
Publisher: Springer Verlag (Germany)
Publication year: 1985
Volume: 13
Journal issue: 1
Pages range: 205-229
ISSN: 0095-4616
Language: English


Abstract


A vibrating plate is here taken to satisfy the model equation:utt + Δ2u = 0 (whereΔ2u:= Δ(Δu); Δ = Laplacian) with boundary conditions of the form:uv = 0 and(Δu)v = ϕ = control. Thus, the state is the pair [u, ut] and controllability means existence ofϕ on Σ:= (0,T∂Ω transfering ‘any’[u, ut]0 to ‘any’[u, ut]T. The formulation is given by eigenfunction expansion and duality. The substantive results apply to a rectangular plate. For largeT one has such controllability with∥ϕ∥ = O(T−1/2). More surprising is that (based on a harmonic analysis estimate [11]) one has controllability for arbitrarily short times (in contrast to the wave equation:utt = Δu) with log∥ϕ∥ = O(T−1) asT→0. Some related results on minimum time control are also included.





This research was partially supported under the grant AFOSR-82-0271.





Communicated by I. Lasiecka





 



FAU Authors / FAU Editors

Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik


External institutions with authors

University of Maryland, Baltimore County


How to cite

APA:
Leugering, G., Krabs, W., & Seidman, T.I. (1985). ON BOUNDARY CONTROLLABILITY OF A VIBRATING PLATE. Applied Mathematics and Optimization, 13(1), 205-229. https://dx.doi.org/10.1007/BF01442208

MLA:
Leugering, Günter, W. Krabs, and Thomas I. Seidman. "ON BOUNDARY CONTROLLABILITY OF A VIBRATING PLATE." Applied Mathematics and Optimization 13.1 (1985): 205-229.

BibTeX: 

Last updated on 2018-03-07 at 11:23