@article{404dbdf22e0f420e856340afdf6558cc,
title = "Transient Behavior Analysis of Vibrationally Controlled Nonlinear Parabolic Systems with Neumann Boundary Conditions",
abstract = "In the first part [1] of this work the conditions for the existence of the stabilizing vibrations for a class of distributed parameter systems governed by parabolic partial differential equations with Neumann boundary conditions were derived, and the guidelines for the choice of the vibration parameters that ensure stabilization were given. The present note addresses the transient behavior analysis of vibrationally controlled systems of the same class.",
author = "Joseph Bentsman and Hong, {Keum Shik}",
note = "Funding Information: t 2 0, U(X,O) = u,(x), (1) where U = U(X, t): R(0,l) x R,-t R{"}; A, B E RnXn are constant matrices; A E R{"}' is a vibratile parameter; C: R{"} x R{"} + R{"} is a nonlinear vector function such that C(0, A) = 0; subscripts of u denote corresponding partial derivatives with respect to t and x; the Neumann boundary conditions are given by U,(O, t)= uJ1, t)= 0, t 2 0; and initial condition by u(x, 0) = u,(x). Assuming A fixed, introduce in (1) parametric vibrations as A + A +f(t) (3) work was supported in part by the National Science Foundation Presidential Young Investigator Award under Grant MSS-8957198, and in part by the Electric Power Research Institute Contract EPRI RP-8010-19.",
year = "1993",
month = oct,
doi = "10.1109/9.241587",
language = "English (US)",
volume = "38",
pages = "1603--1607",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "10",
}