Stabilization of the Korteweg-de Vries-Burgers equation with non-periodic boundary feedbacks (Q1871427)

The author studies the problem of global boundary stabilization of the KdVB equation. He shows that there are feedbacks (smooth invertible functions \(g_1,g_2\), \(g_1(0)= g_2(0)= 0\)) such that the boundary conditions \[ u(0, t)= 0,\quad u_x(1,t)= -g_1(u(1,t)),\quad u_{xx}= g_2(u(1,t)) \] guarantee global asymptotic stability in terms of not only the \(L^2\) norm but also the \(H^3\) norm, which ensures boundedness of the solution for \(H^3\) initial data of any sizes.