Maximal Lp-regularity for an abstract evolution equation with applications to closed-loop boundary feedback control problems


In this paper we present an abstract maximal Lp-regularity result up to T=∞, that is tuned to capture (linear) Partial Differential Equations of parabolic type, defined on a bounded domain and subject to finite dimensional, stabilizing, feedback controls acting on (a portion of) the boundary. Illustrations include, beside a more classical boundary parabolic example, two more recent settings: (i) the 3d-Navier-Stokes equations with finite dimensional, localized, boundary tangential feedback stabilizing controls as well as Boussinesq systems with finite dimensional, localized, feedback, stabilizing, Dirichlet boundary control for the thermal equation.

Publication Title

Journal of Differential Equations