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<p>In this paper we study a bilinear optimal control problem related to a 2D chemo-repulsion stationary model with nonlinear production term. Firstly, we prove the existence of strong solutions for each control given; then, for the extremal problem, we prove the existence of at least one global optimal solution. Afterwards, using a generic result on the existence of Lagrange multipliers, we obtain the so-called first-order necessary optimality conditions for local optimal solutions. Furthermore, we discuss an extension of the results to 3D domains.</p>

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A Stationary Chemo-repulsion System with Nonlinear Production and a Bilinear Optimal Control Problem Related

  • 期刊论文

  • 发表日期：

    2025年9月13日

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  • Yankis R. Linares,
  • Exequiel Mallea-Zepeda,
  • Israel Villarreal-Tintaya

摘要

In this paper we study a bilinear optimal control problem related to a 2D chemo-repulsion stationary model with nonlinear production term. Firstly, we prove the existence of strong solutions for each control given; then, for the extremal problem, we prove the existence of at least one global optimal solution. Afterwards, using a generic result on the existence of Lagrange multipliers, we obtain the so-called first-order necessary optimality conditions for local optimal solutions. Furthermore, we discuss an extension of the results to 3D domains.