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A Wave Equation with a Bounded Control on Two Ends for an Arbitrary Time IntervalDiffer. Uravn., 35
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The Wave Equation with a Boundary Control at One End and the Other End Fixed, Differ -
AV Belikov (2010)
Boundary Control by Displacement at One End of a Nonhomogeneous Rod with the Other End Fixed in the Case of Coinciding Times of Passage of a Wave through Each of the Inhomogeneity PartsDiffer. Uravn., 46
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(2011)
Boundary Control by an Elastic Force at One End of a Nonhomogeneous Rod and the Other End Free for the Passage of a Wave through Each of the Nonhomogeneous Parts at the Same Time, Differ -
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Longitudinal Vibrations of a Rod Consisting of Two Segments of Different Densities and Elasticities in the Case of Identical Wave Travel Time on Each Segment , Dokl
- Publisher
- Springer Journals
- Copyright
- Copyright © 2013 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266113060086
- Publisher site
- See Article on Publisher Site
Abstract
We study boundary control in critical time by elastic forces at two ends of an inhomogeneous rod consisting of two parts of distinct densities and elasticities for the case in which the wave propagation time over each of these parts is the same. We present a closed-form expression for the boundary control by elastic forces bringing the originally quiescent stick into a given terminal state specified by a given terminal displacement and a given terminal velocity in a given critical time.
Journal
Differential Equations – Springer Journals
Published: Jul 26, 2013