Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation

By Weijiu Liu, Miroslav Krstic. 2001

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Local exact controllability to the trajectories of the 1-D Kuramoto–Sivashinsky equation☆ (2011, background): “For instance [2,7,21] deal with the stabilization problem and [17] is concerned with the robust control problem.”
Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation (2009, methodology): “In this direction, one finds the papers [1, 6] by Christofides and Armaou where the stabilization via distributed scalar controls is achieved for the KS equation with periodic boundary conditions, and [21] by Liu and Krstic where they proved the stability of (1) with homogeneous Dirichlet boundary c”
Fredholm Transform and Local Rapid Stabilization for a Kuramoto-Sivashinsky Equation (2015, background): “In [18], with the assumption that λ < 4π(2), the authors studied the global stabilization problems of the K-S equation by a nonlinear boundary feedback control.”
Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach (2017, methodology): “Since then, this has been applied to study the stability of parabolic equations in [33,34], of hyperbolic systems in [9,10,17,18,22], of nonlinear parabolic equations in [36], of Korteweg–de Vries equations in [4] and of Kuramoto–Sivashinsky equations in [28].”