Numerical analysis for the controlled degenerate chemotaxis model
DOI:
https://doi.org/10.55630/j.biomath.2025.10.305Keywords:
controlled Keller-Segel model, degenerate diffusion, finite element method, dosing controlAbstract
The control of chemotactic systems is a critical challenge in applied mathematics, with direct implications for biomedical applications such as cancer therapy. In this paper, we investigate a degenerate Keller--Segel model with a spatiotemporal control input, representing the addition or elimination of chemical concentration. The model is discretized using a finite element scheme, and an adjoint-based optimization algorithm is employed to design effective control strategies. Numerical simulations confirm the stability and efficiency of the method: the cost functional and gradient norm decrease rapidly, the error stabilizes at small values, and both cell density and chemoattractant concentration are successfully reduced. These results demonstrate how numerical analysis provides reliable insights into regulating chemotaxis and highlight its potential for guiding therapeutic dosing strategies.
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Copyright (c) 2025 Sarah Serhal, Georges Chamoun, Mazen Saad, Toni Sayah
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