Abstract:
We will study a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production. We prove the existence of weak solutions, and establish a regularity criterion to get global-in-time strong solutions. As a consequence, we deduce the existence of a global optimal solution with bilinear control, and, using a Lagrange multipliers theorem in Banach spaces, we derive first-order necessary optimality conditions for each local optimal solution.