The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model*

• DOI: 10.1007/s11401-006-0568-7
• Publication Date: 2007-11-13T10:22:10Z
• Authors: Xiuqing Chen; Li Chen; Huaiyu Jian
• Keywords: 0101 mathematics; 01 natural sciences

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.