Well-posedness and regularity of boundary feedback parabolic systems

AbstractA general second order parabolic equation is considered with both Dirichlet or mixed (in particular, Neumann) input function acting on the boundary S of the bounded spatial domain Ω. The distinctive new feature is that the input function is demanded to be expressed in feedback form, i.e. as a linear operator (of finite dimensional range) of the solution, continuous from Hs(Ω) into Lp(S), for some non-negative real s and for p ⩾ 1. Well posedness and regularity results of the resulting closed loop system are established in appropriate functions spaces. The results are illustrated by examples of physical interest