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arXiv · 2609.18030

Optimal control via chemotactic sensitivity of a logistic Keller-Segel model

Yacouba Simpore·Mahamadi Warma·Luis P. Yapu
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Abstract

We study an optimal control problem for a two-equations Keller-Segel system on a bounded domain with Neumann boundary conditions, where the chemotactic sensitivity is modulated by a control $f(x,t)$ acting on the taxis flux $\nabla\!\cdot(f\,u\,\nabla v)$. We prove the well-posedness of the state equation under low regularity assumptions. The analysis is based on the study of an $\varepsilon$-regularized problem, the application of Schauder's fixed point theorem, $\varepsilon$-independent, positivity and a priori estimates, the passage to the limit as $\varepsilon \to 0$, and a uniqueness argument. For a cost functional combining trajectory tracking, taxis penalization, control regularization, and terminal objectives, we establish the existence of optimal controls and derive the first-order optimality conditions through a Lagrange multiplier framework, leading to an adjoint system and a variational inequality for the optimal control. A numerical scheme based on spline collocation in space and Runge-Kutta time-stepping is set and implemented. Numerical experiments are performed to simulate the free and controlled dynamics in conservative and non-conservative cases.

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Yacouba Simpore, Mahamadi Warma, Luis P. Yapu. 2026-09-16. Optimal control via chemotactic sensitivity of a logistic Keller-Segel model. https://arxiv.org/abs/2609.18030

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