Work

Finite element approximation of bilinear optimal control for degenerate Keller-Segel model

Year: 2026

Type: article

Abstract: In this paper, we propose a new numerical scheme for a nonlinear degenerate chemotaxis model subject to bilinear optimal control. This model introduces major analytical and numerical challenges due to the lack of regularity in a complex framework. For that, we develop a finite element scheme for the direct and adjoint systems. First, many energy estimates are established to prove the stability of discrete solutions for both problems. Next, we solve the associated optimal control problem using a gradient optimization algorithm to ensure accurate reconstruction of the control. Finally, several numerical experiments are performed to demonstrate the stability and effectiveness of the proposed approach in regulating chemotactic aggregation. Consequently, the reliability of the algorithm confirms the influence of the bilinear control on the chemical dosing strategies.

Source: Computers & Mathematics with Applications

DOI: 10.1016/j.camwa.2026.10.008

Authors: Sarah Serhal, Georges Chamoun, Mazen Saad, Toni Sayah

Institutions: Centre National de la Recherche Scientifique, Saint Joseph University, Laboratoire de Mathématiques Jean Leray

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,170

Funder: Conseil de la Recherche de l'Université Saint-Joseph de Beyrouth