scholarly journals Large time behavior of Euler–Poisson equations for isothermal fluids with spherical symmetry

2010 ◽  
Vol 363 (1) ◽  
pp. 302-309 ◽  
Author(s):  
Huimin Yu
Keyword(s):  
Spherical Symmetry ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Poisson 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.

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 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 well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

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