<p>We develop and analyze a mathematical model for reactive transport in the cathode gas diffusion layers of hydrogen fuel cells. The model couples Darcy flow, continuity, and advection–diffusion equations with boundary conditions that account for electrochemical reactions at the catalyst layer. To enhance performance, we formulate and solve a porosity-based optimization problem that seeks an optimal gas diffusion layer design ensuring both uniform and maximized oxygen distribution. The resulting PDE-constrained optimization problem is solved via finite element methods combined with gradient-based iteration. Numerical results demonstrate that optimized porosity profiles significantly improve oxygen transport uniformity and increase electrochemical reaction rates, compared with constant-porosity designs. The proposed framework provides a rigorous applied-mathematics approach for designing more efficient and durable fuel cell electrodes.</p>