Abstract
This paper treats a water flow regularization problem by means of local boundary conditions for the two-dimensional viscous shallow water equations. Using an a-priori energy estimate of the perturbation state and the Faedo–Galerkin method, we build a stabilizing boundary feedback control law for the volumetric flow in a finite time that is prescribed by the solvability of the associated Cauchy problem. We iterate the same approach to build by cascade a stabilizing feedback control law for infinite time. Thanks to a positive arbitrary time-dependent stabilization function, the control law provides an exponential decay of the energy.
Funder
CIPR
College of Petroleum Engineering and Geosciences at King Fahd University of Petroleum and Minerals
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference38 articles.
1. Aamo, O.M., and Krstic, M. Flow Control by Feedback: Stabilization and Mixing, 2003.
2. Coron, J.-M. Volume 136 of Mathematical Surveys and Monographs. Control and Nonlinearity, 2007.
3. Optimal control of thermally convected fluid flows;Ito;SIAM J. Sci. Comput.,1998
4. Koumoutsakos, P., and Mezic, I. Control of Fluid Flow, 2006.
5. Sritharan, S. Optimal Control of Viscous Flow, 1998.