A REGULARITY CRITERION FOR A 3D CHEMO-REPULSION SYSTEM AND ITS APPLICATION TO A BILINEAR OPTIMAL CONTROL PROBLEM

摘要

In this paper, a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production is studied. The existence of weak solutions is proved, and a regularity criterion to get global-in-time strong solutions is established. As a consequence, the existence of a global optimal solution with bilinear control is deduced, and using a Lagrange multiplier theorem, first-order optimality conditions for local optimal solutions are derived.