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Élder Jesús Villamizar Roa, Professor, Escuela de Matemáticas, Universidad Industrial de Santander (UIS), Bucaramanga, Colombia

Seminar
7 October, 2026, 16:00
Aula B, Palazzo delle Scienze

An optimal control problem related to a Keller-Segel type model describing the gliobastoma growth

Abstract:
In this talk, we present some recent results on an optimal control problem associated with a parabolic Keller–Segel system featuring chemoattraction. The model describes glioblastoma growth in a two-dimensional bounded domain influenced by oxygen levels, with two distinct therapeutic strategies acting as controls: chemotherapy and antiangiogenic treatment. First, we establish a well-posedness framework to ensure the existence and uniqueness of weak–strong solutions to the system. Subsequently, we study the optimal control problem by formulating a cost functional that seeks to minimize both tumor density and therapy-related costs. We prove the existence of a global optimal solution and derive the first-order necessary optimality conditions. Finally, we propose a numerical methodology for approximating the optimal controls.