The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model*
Xiuqing Chen , Li Chen , Huaiyu Jian
Chinese Annals of Mathematics, Series B ›› 2007, Vol. 28 ›› Issue (6) : 651 -664.
The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model*
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.
Quantum drift-diffusion / Weak solution / Long-time behavior / 35k35 / 35J60 / 65M12 / 65M20
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