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

Huaman D.N. · Electronic Journal of Qualitative Theory of Differential Equations (2026) · DOI: 10.14232/ejqtde.2026.1.38

Resumen

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 L2-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.

Instituciones: Universidad Nacional Agraria La Molina