تقرير
Bilinear optimal control for chemotaxis model: The case of two-sidedly degenerate diffusion with Volume-Filling Effect
العنوان: | Bilinear optimal control for chemotaxis model: The case of two-sidedly degenerate diffusion with Volume-Filling Effect |
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المؤلفون: | Chamoun, Georges, Saad, Mazen, Sayah, Toni, Serhal, Sarah |
سنة النشر: | 2024 |
المجموعة: | Computer Science Mathematics |
مصطلحات موضوعية: | Mathematics - Optimization and Control, Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis |
الوصف: | In this paper, we study an optimal control problem for a coupled non-linear system of reaction-diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the concentration of the chemotactic agent. By controlling the concentration of the chemical substrates, this study can guide the optimal growth of cells. The novelty of this work lies on the direct and dual models that remain in a weak setting, which is uncommon in the recent literature for solving optimal control systems. Moreover, it is known that the adjoint problems offer a powerful approach to quantifying the uncertainty associated with model inputs. However, these systems typically lack closed-form solutions, making it challenging to obtain weak solutions. For that, the well-posedness of the direct problem is first well guaranteed. Then, the existence of an optimal control and the first-order optimality conditions are established. Finally, weak solutions for the adjoint system to the non-linear degenerate direct model, are introduced and investigated. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2407.07519 |
رقم الأكسشن: | edsarx.2407.07519 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |