Existence and Stability of Stationary Solutions with Boundary Layers in a Tikhonov-Type System Arising in the Drift-Diffusion Model of Semiconductors of Sub-Debye-Length

This paper investigates stationary boundary-layer solutions of singularly perturbed systems of Tikhonov-type equations arising in drift-diffusion models of sub-Debye semiconductors. Boundary-layer asymptotics for solutions are constructed for Neumann and Dirichlet boundary conditions. The asymptotic method of differential inequalities is used to prove the existence and asymptotic stability theorems for these solutions. A physical interpretation of the results thus obtained is provided.