U. Biccari, V. Hernández-Santamaría Null controllability of a nonlocal heat equation with an additive integral kernel. SIAM J. Control Optim., Vol. 57, No. 4 (2019), pp. 2924-2938, DOI: 10.1137/18M1218431
Abstract: We consider a linear nonlocal heat equation in a bounded domain \Omega\subset\mathbb{R}^d with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when the control acts on a open subset of the domain. It is by now known that the system is null-controllable when the kernel is time-independent and analytic or, in the one-dimensional case, in separated variables. In this paper we relax this assumption and we extend the result to a more general class of kernels. Moreover, we get explicit estimates on the cost of null-controllability.
