scholarly journals ALGEBRAIC TIME DECAY FOR THE BIPOLAR QUANTUM HYDRODYNAMIC MODEL

2008 ◽  
Vol 18 (06) ◽  
pp. 859-881 ◽  
Author(s):  
HAI-LIANG LI ◽  
GUOJING ZHANG ◽  
KAIJUN ZHANG
Keyword(s):  
Decay Rate ◽  
Semiclassical Limit ◽  
Global Solutions ◽  
Time Decay ◽  
Unique Strong Solution ◽  
Algebraic Decay ◽  
Exponential Time ◽  
Qhd Model ◽  
Quantum Hydrodynamic ◽  
Time Decay Rate

The initial value problem is considered in the present paper for the bipolar quantum hydrodynamic (QHD) model for semiconductors in ℝ3. The unique strong solution exists globally in time and tends to the asymptotical state with an algebraic decay rate as time goes to infinity is proved. And, the global solution of linearized bipolar QHD system decays in time at an algebraic decay rate from both above and below is shown. This means that in general we cannot get an exponential time-decay rate for bipolar QHD system, which is different from the case of unipolar QHD model (where global solutions tend to the equilibrium state at an exponential time-decay rate) and is mainly caused by the nonlinear coupling and cancelation between two carriers. Moreover, it is also shown that the nonlinear dispersion does not affect the long time asymptotic behavior, which by product gives rise to the algebraic time-decay rate of the solution of the bipolar hydrodynamical model in the semiclassical limit.

EARLY TIME DEPARTURES FROM THE WEISSKOPF-WIGNER DECAY RATE

1993 ◽  
Vol 08 (24) ◽  
pp. 4355-4367 ◽  
Author(s):  
K. URBANOWSKI ◽  
J. SKOREK
Keyword(s):  
Decay Rate ◽  
State Vector ◽  
Early Time ◽  
Time Decay ◽  
Time Decay Rate

The problem of the early time decay rate is studied using the equation for a projection of a state vector. Formulas are found for the decay rate γ(t), generally depending on time, and for early time departures of γ(t) from a rate γ0, given by Weisskopf-Wigner approximation. It is shown that γ(t)→0 as t→0, and γ(t)→γ0 as t→∞. The dependence γ(t) on t is studied numerically in some models.

Time decay rate for two 3D magnetohydrodynamics- α models

2013 ◽  
Vol 37 (6) ◽  
pp. 838-845 ◽  
Author(s):  
Zaihong Jiang ◽  
Jishan Fan
Keyword(s):  
Decay Rate ◽  
Time Decay ◽  
Time Decay Rate

scholarly journals Optimal time-decay rate of global classical solutions to the generalized compressible Oldroyd-B model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Shuai Liu ◽  
Yuzhu Wang
Keyword(s):  
Decay Rate ◽  
Decay Rates ◽  
Classical Solutions ◽  
Optimal Time ◽  
Time Decay ◽  
Global Classical Solutions ◽  
Time Decay Rates ◽  
Two Space Dimensions ◽  
Time Decay Rate ◽  
Three Space

<p style='text-indent:20px;'>In this paper, we investigate the optimal time-decay rates of global classical solutions for the compressible Oldroyd-B model in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n(n = 2,3) $\end{document}</tex-math></inline-formula>. Global classical solutions in two space dimensions are still open. We first complete the proof of global classical solutions in two space dimensions. Based on global classical solutions and Fourier spectrum analysis, we obtain the optimal time-decay rates of global classical solutions in two and three space dimensions. More precisely, if the initial data belong to <inline-formula><tex-math id="M2">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula>, the optimal time-decay rate of solutions and time-decay rates of <inline-formula><tex-math id="M3">\begin{document}$ l(l = 1,\cdot\cdot\cdot,m) $\end{document}</tex-math></inline-formula> order derivatives under additional assumptions are established.</p>

scholarly journals Long Time Decay Rate to a Bipolar Quantum Drift-Diffusion Model

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Yingjie Zhu ◽  
Bo Liang ◽  
Xiting Peng
Keyword(s):  
Decay Rate ◽  
Dimensional Space ◽  
Functional Method ◽  
Time Behavior ◽  
Drift Diffusion Model ◽  
One Dimensional ◽  
Entropy Functional ◽  
Long Time ◽  
Quantum Hydrodynamic ◽  
Time Decay Rate

This paper is devoted to studying the long time behavior of solutions to a bipolar quantum hydrodynamic in one-dimensional space for general pressure functions. The model is usually applied to simulate some quantum effects in semiconductor devices. The decay rate for time variable is obtained by the entropy functional method and semidiscrete technique.

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