Boundary null controllability for the heat equation with dynamic boundary conditions

Abstract

<p style='text-indent:20px;'>In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control supported on an arbitrary subboundary. The proof of the main result combines a new boundary Carleman estimate and some regularity estimates for the adjoint system, with an explicit dependence with respect to the final time. This technique allows us to overcome a new difficulty that arises when absorbing a normal derivative term.</p>

Identification of source terms in wave equation with dynamic boundary conditions

“…Such a weight function has not been considered before, up to our knowledge. This issue has recently been resolved in the parabolic case [10] by regularity estimates. Thus, we believe that this open question deserves more attention, in contrast to [16,Remark 3].…”