A Best Cost of Null Controllability for the 1D Heat Equation by Strategic Zone Profile

This study is the third step of a project on the null controllability of the 1D heat equation. First, we show a boundary and internal results of controllability by a new approach using a linear, continuous, and surjective operator built from the solution of the heat system. Second, we improve the minimum time of null controllability of the 1D heat equation by using the notion of strategic zone actuators. So, we managed to improve the minimal time of null controllability to the 1D heat equation. In this study, the best minimum cost of null controllability has been estimated for the 1D heat equation based on the minimum controllability time calculated in the second step.