Bilinear optimal control of a reaction-diffusion equation: overcoming boundedness constraints on controls

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 بهمن 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.90287.1538

نویسندگان

Redouane El Mezegueldy^* ؛ Youssef Ouakrim؛ Mohamed Ouzahra

Laboratory MMPA, Department of mathematics and informatics, ENS, University of Sidi Mohamed Ben Abdellah, Fez, Morocco.

چکیده

We study an optimal control problem for bilinear reaction-diffusion equations. The novelty of our approach lies in considering controls from the space of essentially bounded functions without imposing a priori bounds on the admissible set. We introduce an auxiliary problem with controls in $L^p$ spaces ($p > 1 + N/2$, where $N$ is the spatial dimension) and demonstrate that both formulations are equivalent in terms of optimal solutions. Under suitable assumptions on the system parameters, we establish the existence of optimal controls and derive first-order optimality conditions. Our theoretical findings are supported by numerical simulations that validate the practical effectiveness of the proposed approach. This work provides a new framework for handling bilinear control problems without artificial constraints, offering potential applications in population dynamics and ecological management.

کلیدواژه‌ها

Bilinear optimal control؛ Reaction-diffusion equations؛ Essentially bounded controls؛ Optimality conditions