Existence Of Weak Solution And Semiclassical Limit Of An Isentropic Unipolar Drift-Diffusion Model Of Semiconductor

This paper studies the existence of weak solution and the semiclassical limit of the isentrop-ic quantum drift-diffusion model in a bounded domain Ω∈R(N≥2) with Lipschitz boundary condition.In the first part, the semidiscretization in time is used to solve the existence of the solution of the following model under the conditions where α>0, Ω is a bounded domain with Lipschitz boundary in RN, the v denotes the outer normal vector and the time T>0. n=n(x, t) represents the density of the electron and V=V(x, t) is the electrostatic potential, and the positive constants ε, λ,θ denote the scaled Planck constant, the Debye length and temperature respectively which are parameters.In the second part of this paper, we are going to investigate the semiclassical limit of the weak solution to the model above, i,e. the relationship of the weak solution between the above model and the quantum drift-diffusion model below when the εâ†'0:...