Asymptotic behaviour of the solutions and optimal location of the actuator for the pointwise stabilization of a string
By K. Ammari, Antoine Henrot, Marius Tucsnak. Asymptotic Analysis, 2001
88 citations recorded by the source corpus.
We study the large time behavior of the solutions of a homogenous string equation with a homogenous Dirichlet boundary condition at the left end and a homogenous Neuman boundary condition at the right end. A pointwise interior actuator gives a linear viscous damping term. We give a complete characterization of the positions of the actuator for which the system becomes exponentially stable in the energy space. In the case of nonexponential decay in the energy space we give explicit polynomial decay estimates valid for regular initial data. Moreover we show that the fastest decay rate is obtained if the actuator is located at the middle point of the string.
Subfields: Computational Mechanics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/8ce4c065040182a8890c9a645416b771e8a39dee
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In Computational Mechanics
In Control and Systems Engineering
- Kais Ammari
- Marius Tucsnak
- Enrique Zuazua
- Serge Nicaise
- Luc Miller
- Sylvain Ervedoza
- Julie Valein
- George Weiss
Citations in the corpus
- Stabilization of second order evolution equations by a class of unbounded feedbacks (2001, methodology): “Remark 5.5. The same method can be applied for a string with dierent boundary conditions (see Ammari et al. [ 2 ]).”
- Feedback stabilization of a class of evolution equations with delay (2009, unknown): “, [1–6,11,26,28].”