Rapid Fredholm stabilization of the Kuramoto--Sivashinsky equation with unrestricted, spatially-varying anti-diffusion

תקציר מקורי באנגליתarXiv:2610.08764v1 Announce Type: cross Abstract: We develop the first feedback design for rapid stabilization of the Kuramoto--Sivashinsky equation with a spatially varying anti-diffusion coefficient. For constant coefficients, the single-input Fredholm design of Coron and L\"u (2015) excludes a discrete set of values at which repeated unstable eigenvalues cause a loss of controllability. We overcome this obstruction by introducing a second boundary input and assigning the two inputs distinct roles. The key idea, inspired by Heymann's Lemma, is to use the boundary value $u(0,t)$ entirely for a pre-feedback that renders the modified plant controllable through the curvature input $u_{xx}(0,t)$. The latter input then stabilizes the plant through a Fredholm backstepping transformation. We sho