Dirichlet-Neumann Problem for Unipolar Isentropic Quantum Drift-Diffusion Model

摘要

This paper studies the existence,semiclassical limit,and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model,a fourth order parabolic system.Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary con-dition.Furthermore,the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.