Boundary Feedback Stabilization of Two-Dimensional Shallow Water Equations with Viscosity Term

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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.
Funding Information
  • CIPR (Center for Integrative Petroleum Research)
  • College of Petroleum Engineering and Geosciences at King Fahd University of Petroleum and Minerals

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