A regularity criterion for a 3D chemo-repulsion system and its application to a bilinear optimal control problem

2018/08/26 by Guillén-González, Francisco, Mallea-Zepeda, Exequiel, Rodríguez-Bellido, María Ángeles
#35K51 #35Q92 #49J20 #49K20 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1808.09294

Abstract

In this paper we study a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production. We prove the existence of weak solutions and we 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, we derive first-order optimality conditions for local optimal solutions.

Related

• Optimal bilinear control problem related to a chemo-repulsion system in\n 2D domains
• On a bi-dimensional chemo-repulsion model with nonlinear production
• Study of a chemo-repulsion model with quadratic production. Part I: Analysis of the continuous problem and time-discrete numerical schemes
• Optimal control related to weak solutions of a chemotaxis-consumption model
• Bilinear optimal control for chemotaxis model: The case of two-sidedly degenerate diffusion with Volume-Filling Effect