Exact null controllability of the Lobesia botrana model with diffusion

This paper is devoted to analyze the exact null controllability of the diffusive Lobesia botrana model with nonlocal boundary condition. We study the null controllability of butterfly population by acting on eggs, larvas and female moths in a small age interval. We assume that the control of female moths is in a certain given region of the vineyard. The main result is established by combining some estimations and the Carleman inequality for the backward system related to an optimal control problem. A fixed point theorem is then used to draw the conclusion.