@article{CHEN2008, 
author = {Li CHEN and Xiuqing CHEN},
title = {Dirichlet-Neumann Problem for Unipolar Isentropic Quantum Drift-Diffusion Model},
year = {2008},
journal = {Tsinghua Science and Technology},
volume = {13},
number = {4},
pages = {560-569},
keywords = {weak solution, exponential decay, quantum drift-diffusion, fourth order parabolic system, semiclassical limit},
url = {https://www.sciopen.com/article/10.1016/S1007-0214(08)70089-0},
doi = {10.1016/S1007-0214(08)70089-0},
abstract = {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 condition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.}
}