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Stabilization of Second Order Evolution Equations with Unbounded Feedback with Delay

  • Kaïs Ammari
  • Serge Nicaise
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2124)

Abstract

We now turn to problems with delays, namely in the same Hilbert setting than in the previous chapter we consider the closed loop system (5): \(\displaystyle{ \left \{\begin{array}{c} x^{{\prime\prime}}(t) + \mathit{Ax}(t) + B_{1}B_{1}^{{\ast}}x^{{\prime}}(t) + B_{2}B_{2}^{{\ast}}x^{{\prime}}(t-\tau ) = 0,\,t > 0 \\ x(0) = x^{0},\,x^{{\prime}}(0) = x^{1}, \\ B_{2}^{{\ast}}x^{{\prime}}(t-\tau ) = f^{0}(t-\tau ),\,0 < t <\tau.\end{array} \right. }\)

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Kaïs Ammari
    • 1
  • Serge Nicaise
    • 2
  1. 1.Dept of Mathematics Faculty of SciencesUniversity of MonastirMonastirTunisia
  2. 2.Lab. de Mathématiques et de leurs applications de Valenciennes (LAMAV)Univ. de Valenciennes et du Hainaut CambrésisValenciennesFrance

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