Global Boundary Stabilization of the Korteweg-de Vries-Burgers Equation

The problem of global exponential stabilization by boundary feedback for the Korteweg-de Vries-Burgers equation on the domain [0, 1] is considered. We derive a control law of the form u(0) = ux(1) = uxx(1) − k[u(1)3 + u(1)] = 0, where k is a sufficiently large positive constant, and prove that it guarantees L2-global exponential stability, H3-global asymptotic stability, and H3-semiglobal exponential stability. Our decay rate estimates depend not only on the diffusion coefficient but also on the dispersion coefficient. The closed-loop system is shown to be well posed.

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