ON BOUNDARY CONTROLLABILITY OF A VIBRATING PLATE

Leugering G, Krabs W, Seidman TI (1985)


Publication Language: English

Publication Status: Published

Publication Type: Journal article

Publication year: 1985

Journal

Publisher: Springer Verlag (Germany)

Book Volume: 13

Pages Range: 205-229

Journal Issue: 1

URI: http://link.springer.com/article/10.1007/BF01442208

DOI: 10.1007/BF01442208

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.

 

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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://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.

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