We consider the problem of stabilizing the bilayer \textit{Saint-Venant}model, which is a coupled system of two rightward and two leftward convectingtransport partial differential equations (PDEs). In the stability proofs, weemploy a Lyapunov function in which the parameters need to be successivelydetermined. To the best of the authors' knowledge, this is the first time thiskind of Lyapunov function is employed, and this result is the first one on thestabilization of the linearized bilayer \textit{Saint-Venant} model. Numericalsimulations of the bilayer \textit{Saint-Venant} problem are also provided toverify the result.
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