Maximal Lp-regularity of abstract evolution equations modeling closed-loop, boundary feedback control dynamics

Abstract

We provide maximal 𝐿𝑝-regularity up to the level 𝑇 < ∞ or 𝑇 = ∞ of an abstract evolution equation in Banach space, which captures boundary closed-loop parabolic systems, defined on a bounded multidimensional domain, with finitely many boundary control vectors and finitely many boundary sensors/actuators. Illustrations given include classical parabolic equations as well as Navier-Stokes equations in 𝐿𝑝(Ω) or 𝐿𝑞 𝜎(Ω), respectively.