This study investigates the gradient stabilization of nonlinear systems within a nanolayer boundary region by considering a nonlinear boundary control  Condition. We aim to demonstrate the stabilization of the nanolayer’s boundary gradient using the Lyapunov function approach, under specific regularity assumptions and control conditions. Additionally, we extend the stability analysis to more complex systems by examining the limit problem with interface conditions through the epi-convergence approach. The theoretical results presented in this paper are subsequently validated through numerical testing.