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Journal of Dynamical and Control Systems

, Volume 25, Issue 2, pp 309–309 | Cite as

Correction to: Hierarchical Control for the One-dimensional Plate Equation with a Moving Boundary

  • I. P. de JesusEmail author
  • J. Limaco
  • M. R. Clark
Correction
  • 388 Downloads

Correction to: Journal of Dynamical and Control Systems

 https://doi.org/10.1007/s10883-018-9413-z

The original version of this article unfortunately contained a mistake. On page 653, Equation (5.2) should be
$$ \left| \begin{array}{l} \varphi^{\prime\prime} + L^{*} \varphi = \gamma(t) \psi \ \ \text{in} \ \ Q, \\\psi^{\prime\prime} + L \psi = 0 \ \ \text{in} \ \ Q, \\v^{\prime\prime} + Lv = 0 \ \ \text{in} \ \ Q, \\p^{\prime\prime} + L^{*}p = \gamma(t)(v - v_{2}) \ \ \text{in} \ \ Q, \\\varphi = 0 \ \ \ \text{on} \ \ \ {\Sigma}, \\\varphi_{y} = 0 \ \ \ \text{on} \ \ \ {\Sigma}, \\\psi = 0 \ \ \ \text{on} \ \ \ {\Sigma}, \\\psi_{y} = \left\{ \begin{array}{l} 0 \ \ \text{on} \ \ {\Sigma}_{1},\\ \frac{a(t)}{\sigma}\varphi_{yy} \ \ \text{on} \ \ {\Sigma}_{2},\\ 0 \ \ \text{on} \ \ \ {\Sigma} \backslash {\Sigma}_{0}, \end{array} \right.\\ v_{y} = \left\{ \begin{array}{l} - a(t)\varphi_{yy} \ \ \text{on} \ \ {\Sigma}_{1},\\ \frac{a(t)}{\sigma}p_{yy} \ \ \text{on} \ \ {\Sigma}_{2},\\ 0 \ \ \text{on} \ \ \ {\Sigma} \backslash {\Sigma}_{0}, \end{array} \right.\\ v = 0 \ \ \ \text{on} \ \ \ {\Sigma}, \\p = 0 \ \ \ \text{on} \ \ \ {\Sigma}, \\p_{y} = 0 \ \ \ \text{on} \ \ \ {\Sigma}, \\\varphi(.,T) = f^{0}, \varphi^{\prime}(.,T) = f^{1} \ \ \text{in} \ \ {\Omega}, \\v(0) = v^{\prime}(0) = 0 \ \ \text{in} \ \ {\Omega}, \\p(T) = p^{\prime}(T) = 0 \ \ \text{in} \ \ {\Omega}. \end{array} \right. $$

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universidade Federal do Piauí, DMTeresinaBrazil
  2. 2.Universidade Federal Fluminense, IMENiteróiBrazil

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