Local explicit feedback boundary conditions are given for the stabilization in L2−norm of the 2-D shallow
water model. The proposed method is based on symmetrization of the flux matrices of the linearized model and analysis of the Riemann invariants. The non-conservative 2-D shallow water equations are linearized around the target steady state sub-critical flow. The established feedback control laws guarantee a decay of the energy of the perturbation model.
We present numerical simulations to demonstrate how the proposed controller works for the linearized as well as nonlinear shallow water problem.

DOI 10.1007/s40435-013-0006-0