New arXiv preprint on infinite-dimensional systems
In our new arXiv preprint, we study the equation governing the small vibrations of a stretched fluid-conveying pipe in a star-shaped network. We examine the question exponential stabilisability of such a system by means of feedback control torques applied at the inner vertex of the system. An approach to the study of the stabilisability problem for the closed-loop system is presented using the spectral approach previously introduced by the authors for star graphs of beams. When the tension in the pipes is very large compared to fluid-flow velocity, we establish a positive result that gives exponential decay of the energy of solutions of the closed-loop system.
Read more about the Infinite-Dimensional Systems group here.