On The Existence And Uniqueness Of Weak Solutions To A Degenerate Drift-Diffusion Model For Semiconductors

Abstract: In this paper we study the following problemwith the initial and boundary conditonswhere the unknowns ψ, n and p denote the electrostatic potential, the electron density and the hole density respectively, J_n and J_p represent the current density of the concentrations. And the following model with temperature effect is also studied in this paperWe investigate the steady-state and time-dependent cases of the problem, respectively. We prove the existence of the solutions of steady-state and time-dependent, and we present also the uniqueness of time-dependent solution. The paper is organized in the following way :In chapter 1, we discuss the existence of the steady-state solution. We make a regularization of the problem by a cut-off method first, and prove the existence of the solution of the regularized problem with the fixed point theorem. Then we prove the solution of the regularized problem is also the solution of the original problem after an estimate. In chapter 2 the time-dependent model for semiconductor devices is studied. We still regularize the problem by applying cut-off method. Then by Moser's iteration technique we obtain the L~∞ estimates of the solutions of the regularized problem and prove that the limit of the solutions of the regularized problem is a solution of the original problem. In the end we show the time-dependent solution is unique under . Finally, the existence of weak solutions to the model with temperature effect is obtained by the similar methods in chapter 3.