scholarly journals A Sharp Estimate of Entropy Solution to Euler-Poisson System for Semiconductors in the Whole Domain

2019 ◽  
pp. 1-12
Author(s):  
Yanqiu Cheng ◽  
Xixi Fang ◽  
Huimin Yu
Keyword(s):  
Large Time ◽  
Approximate Solutions ◽  
Entropy Inequality ◽  
Large Time Behavior ◽  
Doping Profile ◽  
Entropy Solutions ◽  
Time Behavior ◽  
One Dimensional ◽  
Poisson Equations ◽  
The One

In this paper, we are concerned with the global existence, large time behavior, and timeincreasing-rate of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations. When the adiabatic index γ > 2, the L∞ estimates of artificial viscosity approximate solutions are obtained by using entropy inequality and maximum principle. Then the L∞ compensated compactness framework demonstrates theconvergence of approximate solutions. Finally, the global entropy solutions are proved to decay exponentially fast to the stationary solution, without any assumption on the smallness of initial data and doping profile.

scholarly journals Global Existence and Large Time Behavior of Solutions to the Bipolar Nonisentropic Euler-Poisson Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Min Chen ◽  
Yiyou Wang ◽  
Yeping Li
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Negative Ion ◽  
Initial Mass ◽  
Far Field ◽  
Time Behavior ◽  
Poisson Equations ◽  
Global Smooth Solutions ◽  
The Difference ◽  
The One

We study the one-dimensional bipolar nonisentropic Euler-Poisson equations which can model various physical phenomena, such as the propagation of electron and hole in submicron semiconductor devices, the propagation of positive ion and negative ion in plasmas, and the biological transport of ions for channel proteins. We show the existence and large time behavior of global smooth solutions for the initial value problem, when the difference of two particles’ initial mass is nonzero, and the far field of two particles’ initial temperatures is not the ambient device temperature. This result improves that of Y.-P. Li, for the case that the difference of two particles’ initial mass is zero, and the far field of the initial temperature is the ambient device temperature.

scholarly journals Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yan Li ◽  
Yanqiu Cheng ◽  
Huimin Yu
Keyword(s):  
Hydrodynamic Model ◽  
Variable Coefficient ◽  
Large Time ◽  
Large Time Behavior ◽  
Entropy Solutions ◽  
Time Behavior ◽  
Viscosity Method ◽  
One Dimensional ◽  
Bounded Interval ◽  
Uniform Estimates

In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the uniform estimates of density, we then prove the entropy solutions converge to the corresponding unique stationary solution exponentially with time. We generalize the existing results to the variable coefficient damping case.

Optimal decay rates on the solution to the compressible gas–liquid drift-flux model with slip

2017 ◽  
Vol 28 (02) ◽  
pp. 337-386 ◽  
Author(s):  
Guangyi Hong ◽  
Changjiang Zhu
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Decay Rates ◽  
Time Behavior ◽  
One Dimensional ◽  
Drift Flux Model ◽  
Drift Flux ◽  
Flux Model ◽  
The One ◽  
Compressible Gas

In this paper, the large time behavior of the solution to the initial-boundary problems for the one-dimensional compressible gas–liquid drift-flux model with slip is studied. Under some suitable smallness conditions upon the initial data, the optimal pointwise upper and lower decay estimates on masses as well as the sharpest decay rates for the norms in terms of the velocity function are obtained. This result generalizes the one in [On the large time behavior of the compressible gas–liquid drift-flux model with slip, Math. Models Methods Appl. Sci. 25 (2015) 2175–2215] by Evje and Wen. The key of the proof is to derive some new global-in-time weighted estimates. Our method can also be easily adopted to the study on the large time behavior of the solution to the one-dimensional compressible Naiver–Stokes equations.

LARGE TIME DECAY OF SOLUTIONS TO ISENTROPIC GAS DYNAMICS WITH SPHERICAL SYMMETRY

2009 ◽  
Vol 06 (02) ◽  
pp. 371-387
Author(s):  
NAOKI TSUGE
Keyword(s):  
Spherical Symmetry ◽  
Gas Dynamics ◽  
Large Time ◽  
Approximate Solutions ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Time Decay ◽  
Decay Of Solutions ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

We consider the large time behavior of solutions to isentropic gas dynamics with spherical symmetry. In the present paper, we show the decay of the pressure in particular. To do this, we investigate approximate solutions constructed by a difference scheme.

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