Biccari U., Hernández-Santamaría V. Null controllability of a nonlocal heat equation with integral kernel, DOI:
Abstract: We consider a linear nonlocal heat equation in a bounded domain 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.