Insensitizing controls for a nonlocal-in-time semilinear heat equation

In this paper, a nonlocal-in-time semilinear heat equation is studied. The goal of this paper is prove the existence of insensitizing controls for a function that depends on the L 2 -norm of solutions of the nonlocal-in-time semilinear heat equation. This problem is equivalent to the null controllability result for a nonlinear cascade system of the heat equations with terms that are nonlocal in time. To prove the null controllability of this nonlinear cascade system, we first obtained a Carleman inequality for an adjoint system, and after, we use Liusternik's theorem.