ON BOUNDARY CONTROLLABILITY OF ONE-DIMENSIONAL VIBRATING SYSTEMS BY W(0)1,P-CONTROLS FOR p∈[2, ∞]
Krabs W, Leugering G (1994)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1994
Journal
Publisher: Wiley-Blackwell
Book Volume: 17
Pages Range: 77-93
Journal Issue: 2
URI: http://onlinelibrary.wiley.com/doi/10.1002/mma.1670170202/abstract
Abstract
This paper is concerned with boundary control of one-dimensional vibrating media whose motion is governed by a wave equation with a 2n-order spatial self-adjoint and positive-definite linear differential operator with respect to 2n boundary conditions. Control is applied to one of the boundary conditions and the control function is allowed to vary in the Sobolev space W
, p for p∈[2, ∞] With the aid of Banach space theory of trigonometric moment problems, necessary and sufficient conditions for null-controllability are derived and applied to vibrating strings and Euler beams.
For vibrating strings also, null-controllability by L(p)-controls on the boundary is shown by a direct method which makes use of d'Alembert's solution formula for the wave equation.
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How to cite
APA:
Krabs, W., & Leugering, G. (1994). ON BOUNDARY CONTROLLABILITY OF ONE-DIMENSIONAL VIBRATING SYSTEMS BY W(0)1,P-CONTROLS FOR p∈[2, ∞]. Mathematical Methods in the Applied Sciences, 17(2), 77-93. https://doi.org/10.1002/mma.1670170202
MLA:
Krabs, W., and Günter Leugering. "ON BOUNDARY CONTROLLABILITY OF ONE-DIMENSIONAL VIBRATING SYSTEMS BY W(0)1,P-CONTROLS FOR p∈[2, ∞]." Mathematical Methods in the Applied Sciences 17.2 (1994): 77-93.
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