SIAM Journal on Control and Optimization, Vol.58, No.3, 1457-1490, 2020
A REGULARITY CRITERION FOR A 3D CHEMO-REPULSION SYSTEM AND ITS APPLICATION TO A BILINEAR OPTIMAL CONTROL PROBLEM
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.
Keywords:chemo-repulsion and production model;weak solutions;strong solutions;bilinear optimal control;optimality conditions