Averaged controllability of the Klein-Gordon equation with a parametric electromagnetic potential

Resumo

In this paper, we consider the average null controllability problem for a Klein-Gordon equation with an electromagnetic potential, which depends on a parameter, that represents the electromagnetic field properties. These properties are affected by many dierent factors related to the behavior of particles.
Thus, to achieve the desired result, we apply the Hilbert Uniqueness Method, which provides direct and inverse averaged inequalities. These inequalities assume the continuity and coercivity of a constructed operator, this entails establishing a parameter independent control that brings the average (with respect to the parameter) of the system to zero.