摘要
The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.
The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model, a fourth order parabolic system. Using semi-discretization in time and entropy estimate, the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann （or periodic） boundary conditions. Furthermore, by a logarithmic Sobolev inequality, it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.
基金
Project supported by the National Natural Science Foundation of China(Nos.10631020,10401019)
the Basic Research Grant of Tsinghua University.
关键词
弱解
两极量子转移模型
长期性
存在性
Quantum drift-diffusion, Weak solution, Long-time behavior
