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): \(\displaystyle{ \left \{\begin{array}{c} x^{{\prime\prime}}(t) + \mathit{Ax}(t) + B_{1}B_{1}^{{\ast}}x^{{\prime}}(t) + B_{2}B_{2}^{{\ast}}x^{{\prime}}(t-\tau ) = 0,\,t > 0 \\ x(0) = x^{0},\,x^{{\prime}}(0) = x^{1}, \\ B_{2}^{{\ast}}x^{{\prime}}(t-\tau ) = f^{0}(t-\tau ),\,0 < t <\tau.\end{array} \right. }\)
Keywords
- Unbounded Feedbacks
- Order Evolution Equations
- Hilbert Setting
- Closed-loop System
- Explicit Decay Rate
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Ammari, K., Nicaise, S. (2015). Stabilization of Second Order Evolution Equations with Unbounded Feedback with Delay. In: Stabilization of Elastic Systems by Collocated Feedback. Lecture Notes in Mathematics, vol 2124. Springer, Cham. https://doi.org/10.1007/978-3-319-10900-8_3
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DOI: https://doi.org/10.1007/978-3-319-10900-8_3
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