A parabolic system model for the formation of porous silicon: Existence, uniqueness, and stability

In this paper, a nonlinear weakly coupled parabolic system is constructed to model porous silicon formation. The model considers physical and chemical factors such as charge carriers transport, ions transport, electrochemical reactions, and material balance. In order to prove the existence of a unique solution for the proposed parabolic model with zero Neumann boundary, we use a monotone method based on the upper and lower solutions. The asymptotic stability of the steady-state solution is also demonstrated, and the behavior of this model is shown for specific cases where the analytical stationary solution is known. Finally, a discussion of the results is carried out, and we conclude that the proposed model reproduces important qualitative features which are observed experimentally.