Integral-type approximate controllability of linear parabolic integro-differential equations

This paper addresses the study of the integral-type approximate controllability of linear parabolic integro-differential equations. This new controllability is defined by imposing some additional integral-type constraints on the usual approximate controllability and therefore, can be used to keep the state close to the target. The paper is concerned with a special choice of integral kernels, which are multiples of the same exponential function. We reduce the problem of new controllability to the obtention of a unique continuation property for the suitable adjoint system.