Numerical analysis for the controlled degenerate chemotaxis model

Résumé fourni par la source

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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