Representation and Control of Infinite Dimensional Systems, 2nd Edition

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Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system (2009, background): “is an isomorphism, see [6], Chapter 3, Theorem 2.”
Navier–Stokes equations with delays on unbounded domains (2006, neutral): “∫ t 0 ‖g(s, us)− g(s, vs)‖2Y ds ≤ Cg ∫ t −h ‖u(s)− v(s)‖2X ds. Observe that (I)-(III) imply that given u ∈ C0([−h, T ]; X), the function gu : t ∈ [0, T ] → Y defined by gu(t) = g(t, ut) ∀ t ∈ [0, T ], is measurable (see Bensoussan et al. 1992) and, in fact, belongs to L∞(0, T ;Y ).”
Carleman estimates for degenerate parabolic operators with applications to null controllability (2006, background): “Controllability theory has been widely investigated for parabolic equations over the last forty years—to the point that it is now the object of several comprehensive expositions, see, e.g., [ 3 ], [14] and [26].”