Optimal control via chemotactic sensitivity of a logistic Keller-Segel model
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 ∇ ·(f u ∇ v). We prove the well-posedness of the state equation under low regularity assumptions. The analysis is based on the study of an ε-regularized problem, the application of Schauder's fixed point theorem, ε-independent, positivity and a priori estimates, the passage to the limit as ε → 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.
Related
- Well-posedness of 2D stochastic parabolic-parabolic Keller-Segel system with logistic source
- Optimal Spectral Lower Bounds and Nonradial Nonlinear Asymptotic Stability of a Family of Three-Dimensional Keller--Segel Self-Similar Blow-Up Solutions
- Optimal strong convergence of a splitting mixed finite element method for a stochastic Keller--Segel system
- Chemotaxis models with signal-dependent sensitivity and a logistic-type source, III: Bifurcation and spike-like solutions
- Optimal Sensitivity of the general Wheatstone Bridge
BibTeX
@misc{simpore2026optimal,
title = {{Optimal control via chemotactic sensitivity of a logistic Keller-Segel model}},
author = {Yacouba Simpore and Mahamadi Warma and Luis P. Yapu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18030},
eprint = {2609.18030},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18030},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal control via chemotactic sensitivity of a logistic Keller-Segel model
AU - Yacouba Simpore
AU - Mahamadi Warma
AU - Luis P. Yapu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18030
UR - https://arxiv.org/abs/2609.18030
AB - 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 ∇ ·(f u ∇ v). We prove the well-posedness of the state equation under low regularity assumptions. The analysis is based on the study of an ε-regularized problem, the application of Schauder's fixed point theorem, ε-independent, positivity and a priori estimates, the passage to the limit as ε → 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.
ER -