共查询到19条相似文献,搜索用时 62 毫秒
1.
黎野平 《数学年刊A辑(中文版)》2007,(1)
对一类有短的动量松弛时间的多维等熵流体动力学半导体模型的极限问题进行了讨论.首先构造非线性问题的有初始层的近似解,进而,在归结问题的解存在且有合适的正则性的假设下,证明了原非线性问题的局部古典解的存在性,并且证明了这个解在归结问题解的存在时间区间内收敛到形式近似解. 相似文献
2.
研究一类半导体磁流体动力学模型,它是由关于电子的质量和速度的守恒律方程耦合Maxwell方程构成的流体动力学方程组.在小初值条件下,运用经典的双曲能量方法,得到了磁流体动力学模型Cauchy问题经典解的整体适定性. 相似文献
3.
对反应扩散方程提出一种新型的Newton波形松弛方法,并给出此方法的误差估计式.通过与传统的波形松弛方法比较,这种Newton波形松弛方法有更快的收敛性,且收敛速度不随网格加密而减慢.这种方法可以保持传统波形松弛方法可并行的特点.最后通过数值算例验证这种方法的有效性. 相似文献
4.
一类半线性积分微分方程初值问题之整体解的存在性与唯一性 总被引:1,自引:0,他引:1
本文运用能量廷拓方法,讨论了一类描述有内部热耗散的杆中热传导问题的半线性积分微分方程初值问题之整体古典解的存在性,并附带证明了该问题之古典解的唯一性。 相似文献
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本文讨论了能量方程是压力一密度关系的一维半导体流体动力学模型方程,通过把欧拉-泊松方程变成拟线性波动方程,利用拟线性波动方程的局部解存在性,得到一维半导体流体动力学模型的局部解,并且解是有界的。 相似文献
7.
林正国 《数学年刊A辑(中文版)》1997,(2)
文中利用不可压缩理想磁流体力学(IMHD)方程组的特殊结构,引入变量代换,证明场论中的有关恒等式,克服失去双曲性所带来的困难,得到了一致能量估计,构造迭代序列,证明了当Alfven数0时,解的奇异极限. 相似文献
8.
本文讨论了一类三维非等熵半导体方程. 利用能量估计法, 证明了热平衡稳态解的存在唯一性.然后, 得到了Cauchy-Neumann问题光滑解的整体存在性以及当t→ +∞这种光滑解以指数速度收敛到稳定解, 改进了文献[12]的结果. 相似文献
9.
通过渐近展开的方法,研究了等离子体中带小参数的双极Euler-Poisson方程的拟中性极限和零松弛时间极限问题.对于每一个极限,只要具有好准备的初值,就可以得到任意阶渐近展开的存在唯一性,并在最后讨论了这些极限的验证问题. 相似文献
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Li-Ming Yeh 《Mathematical Methods in the Applied Sciences》1996,19(18):1489-1507
This paper concerns the well-posedness of the hydrodynamic model for semiconductor devices, a quasi-linear elliptic–parbolic–hyperbolic system. Boundary conditions for elliptic and parabolic equations are Dirichlet conditions while boundary conditions for the hyperbolic equations are assumed to be well-posed in L2 sense. Maximally strictly dissipative boundary conditions for the hyperbolic equations satisfy the assumption of well-posedness in L2 sense. The well-posedness of the model under the boundary conditions is demonstrated. 相似文献
12.
Ingenuin Gasser Ling HsiaoPeter A. Markowich Shu Wang 《Journal of Mathematical Analysis and Applications》2002,268(1):184-199
The limit of the vanishing Debye length (the charge neutral limit) in a nonlinear bipolar drift-diffusion model for semiconductors without a pn-junction (i.e., with a unipolar background charge) is studied. The quasi-neutral limit (zero-Debye-length limit) is determined rigorously by using the so-called entropy functional which yields appropriate uniform estimates. 相似文献
13.
The combined quasineutral and relaxation time limit for a bipolar hydrodynamic model is considered. The resulting limit problem
is a nonlinear diffusion equation describing a neutral fluid. We make use of various entropy functions and the related entropy
productions in order to obtain strong enough uniform bounds. The necessary strong convergence of the densities is obtained
by using a generalized version of the “div-curl” Lemma and monotonicity methods. 相似文献
14.
The combined quasineutral and relaxation time limit for a bipolar hydrodynamic model is considered. The resulting limit problem
is a nonlinear diffusion equation describing a neutral fluid. We make use of various entropy functions and the related entropy
productions in order to obtain strong enough uniform bounds. The necessary strong convergence of the densities is obtained
by using a generalized version of the “div-curl” Lemma and monotonicity methods.
Received September 27, 2001; in revised form February 25, 2002 相似文献
15.
Kaijun Zhang 《偏微分方程(英文版)》1999,12(4):369-383
In this paper we are concerned with the global existence of weak solutions of the Cauchy problem for a simplified one-dimensional hydrodynamic model for semiconductors. Convergence of approximate solutions derived by the fractional step Lax-Friedrichs scheme is established by using the compensated compactness method. 相似文献
16.
Xiao-chun WU 《应用数学学报(英文版)》2023,39(1):95-108
In 2003, Gasser-Hsiao-Li [JDE(2003)] showed that the solution to the bipolar hydrodynamic model for semiconductors(HD model) without doping function time-asymptotically converges to the diffusion wave of the porous media equation(PME) for the switch-off case. Motivated by the work of Huang-Wu[arXiv:2210.13157], we will confirm that the time-asymptotic expansion proposed by Geng-Huang-Jin-Wu [arXiv:2202.13385] around the diffusion wave is a better asymptotic profile for the HD model in this paper... 相似文献
17.
Giuseppe Alì Giovanni Mascali Vittorio Romano Rosa Claudia Torcasio 《Acta Appl Math》2012,122(1):335-348
In this paper we present a hydrodynamical model which, in principle, is able to describe charge transport in a generic compound semiconductor. The model makes use of an analytic approximation for the conduction bands. Energy dispersion relationships in the neighbors (valleys) of the lowest minima are, in fact, taken to be spherical, nonparabolic. The model considers the main scattering mechanisms in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk GaN and SiC. 相似文献
18.
本文研究无Pn-联结的非线性双极半导体漂流扩散模型的消失Debye长度极限(即粒子中性极限)问题.使用熵方法和弱紧性方法从数学上严格证明了快扩散情形的拟中性极限. 相似文献
19.
We study the relaxation limit for the Aw-Rascle system of traffic flow. For this we apply the theory of invariant regions and the compensated compactness method to get global existence of Cauchy problem for a particular Aw-Rascle system with source, where the source is the relaxation term, and we show the convergence of this solutions to the equilibrium state. 相似文献