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

Applied Mathematics and Optimization Springer Verlag (Germany)

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:u_tt + Δ²u = 0 (whereΔ²u:= Δ(Δu); Δ = Laplacian) with boundary conditions of the form:u_v = 0 and(Δu)_v = ϕ = control. Thus, the state is the pair [u, u_t] and controllability means existence ofϕ on Σ:= (0,T)×∂Ω transfering ‘any’[u, u_t]₀ to ‘any’[u, u_t]_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:u_tt = Δu) with log∥ϕ∥ = O(T⁻¹) asT→0. Some related results on minimum time control are also included.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Involved external institutions

University of Maryland, Baltimore County

United States (USA) (US)

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.

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