Global solutions to the Euler-Poisson equations of two-carrier types in one dimension

1997 ◽  
Vol 48 (4) ◽  
pp. 680-693 ◽  
Author(s):  
D. Wang
Keyword(s):  
Global Solutions ◽  
One Dimension ◽  
Poisson Equations

Global Solutions to the One-Dimensional Compressible Navier--Stokes--Poisson Equations with Large Data

2013 ◽  
Vol 45 (2) ◽  
pp. 547-571 ◽  
Author(s):  
Zhong Tan ◽  
Tong Yang ◽  
Huijiang Zhao ◽  
Qingyang Zou
Keyword(s):  
Global Solutions ◽  
Large Data ◽  
Navier Stokes ◽  
One Dimensional ◽  
Poisson Equations ◽  
The One

The a Posteriori Error Estimates for Chebyshev-Galerkin Spectral Methods in One Dimension

2015 ◽  
Vol 7 (2) ◽  
pp. 145-157 ◽  
Author(s):  
Jianwei Zhou
Keyword(s):  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
One Dimension ◽  
A Posteriori ◽  
Error Estimators ◽  
Poisson Equations ◽  
Spectral Approximations ◽  
Fourth Order Equations ◽  
Error Indicators

AbstractIn this paper, the Chebyshev-Galerkin spectral approximations are employed to investigate Poisson equations and the fourth order equations in one dimension. Meanwhile, p-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations. The efficient and reliable a posteriori error estimators are given for different models. Furthermore, the a priori error estimators are derived independently. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error indicators and a priori error estimations.

On the Cauchy problem for one dimension generalized Boussinesq equation

2015 ◽  
Vol 26 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Yinxia Wang
Keyword(s):  
Cauchy Problem ◽  
Boussinesq Equation ◽  
Nonlinear Approximation ◽  
Global Solutions ◽  
One Dimension ◽  
Diffusion Waves ◽  
Self Similar Solution ◽  
The Cauchy Problem ◽  
Nonlinear Diffusion Waves ◽  
Generalized Boussinesq Equation

In this paper, we study the Cauchy problem for one dimension generalized damped Boussinesq equation. First, global existence and decay estimate of solutions to this problem are established. Second, according to the detail analysis for solution operator the generalized damped Boussinesq equation, the nonlinear approximation to global solutions is established. Finally, we prove that the global solution u to our problem is asymptotic to the superposition of nonlinear diffusion waves expressed in terms of the self-similar solution of the viscous Burgers equation as time tends to infinity.

scholarly journals Shock-like solutions of the electrostatic Vlasov equation

1969 ◽  
Vol 3 (1) ◽  
pp. 1-11 ◽  
Author(s):  
David Montgomery ◽  
Glenn Joyce
Keyword(s):  
Electrostatic Potential ◽  
Vlasov Equation ◽  
One Dimension ◽  
Zero Temperature ◽  
Trapped Electrons ◽  
Poisson Equations ◽  
Positive Ions ◽  
Upper Limit ◽  
Fluid Equations

It is shown how to construct shock-like time independent solutions of the electrostatic Vlasov and Poisson Equations in one dimension. The positive ions are assumed to be at zero temperature. The electrostatic potential is assumed to increase monotonically through the shock from zero to a constant value. The most important feature of the solution is a population of trapped electrons in the shocked plasma. In contrast to time-independent solutions based upon fluid equations, there is no upper limit on the amplitude of the shock.

scholarly journals A kinetic chemotaxis model with internal states and temporal sensing

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhi-An Wang
Keyword(s):  
Fourier Transform ◽  
Hydrodynamic Limit ◽  
A Priori ◽  
Global Solutions ◽  
One Dimension ◽  
Chemical Signal ◽  
Chemotaxis Model ◽  
Temporal Gradient ◽  
Internal States ◽  
The Fourier Transform

<p style='text-indent:20px;'>By employing the Fourier transform to derive key <i>a priori</i> estimates for the temporal gradient of the chemical signal, we establish the existence of global solutions and hydrodynamic limit of a chemotactic kinetic model with internal states and temporal gradient in one dimension, which is a system of two transport equations coupled to a parabolic equation proposed in [<xref ref-type="bibr" rid="b4">4</xref>].</p>

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