SEMICLASSICAL LIMIT FOR BIPOLAR QUANTUM DRIFT-DIFFUSION MODEL

Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.     

ASYMPTOTICS OF INITIAL BOUNDARY VALUE PROBLEMS OF BIPOLAR HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

In this paper, we study the asymptotic behavior of the solutions to the bipolar hydrodynamic model with Dirichlet boundary conditions. It is shown that the initial boundary problem of the model admits a global smooth solution which decays to the steady state exponentially fast.     

LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

A one-dimensional quantum hydrodynamic model (or quantum Euler-Poisson system) for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of the steady-state solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.     

多类型模型的Hydrodynamic极限

本文研究一类具有平移不变有限程的变相速率和不同的扩散速率的多类型模型的Hydrodynamic行为。在合适的条件下,证明了该模型的Hydrodynamic极限是一个非线性反应扩散方程的解     

多类型模型的Hydrodynamic极限

本文研究一类具有平移不变有限程的变相速率和不同的扩散速率的多类型模型的Hydrodynamic行为.在合适的条件下,证明了该模型的Hydrodynamic极限是一个非线性反应扩散方程的解.     

A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

In this article, we focus on the short time strong solution to a compressible quantum hydrodynamic model. We establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic model in terms of the gradient of the velocity, the second spacial derivative of the square root of the density, and the first order time derivative and first order spacial derivative of the square root of the density.     

GLOBAL FINITE ENERGY WEAK SOLUTION TO THE VISCOUS QUANTUM NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL MODEL IN 2-DIMENSION

In this paper, we prove the global existence of the weak solution to the viscous quantum Navier-Stokes-Landau-Lifshitz-Maxwell equations in two-dimen- sion for large data. The main techniques are the Faedo-Galerkin approximation and weak compactness theory.     

EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS

The nonlinear viscoelastic wave equation |ut|ρ utt u utt + t 0 g(t s) u(s)ds + |u|p u = 0,in a bounded domain with initial conditions and Dirichlet boundary conditions is considered.We prove that,for a class of kernels g which is singular at zero,the exponential decay rate of the solution energy.The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009.This work improves earlier results.     

非线性波的指数衰减(I)

非线性波的指数衰减（Ｉ）盛其荣（新疆大学，乌鲁木齐市８３００４６）国家自然科学基金资助项目．１９９１年５月２２日收到，１９９１年１１月１１日收到修改稿．一、引言考虑下面问题：其中中的有界开集，边界且存在常数ｃ＞０使中的有界函数且在。内，（５）这里中非...     

OPTIMAL DECAY RATE OF THE COMPRESSIBLE QUANTUM NAVIER-STOKES EQUATIONS

For quantum fluids governed by the compressible quantum Navier-Stokes equations in $\Bbb R^3$ with viscosity and heat conduction, we prove the optimal $L^p-L^q$ decay rates for the classical solutions near constant states. The proof is based on the detailed linearized decay estimates by Fourier analysis of the operators, which is drastically different from the case when quantum effects are absent.     

具指数赋权指标的证券投资多目标线性规划模型

本文提出证券投资决策的指数赋权指标体系．在该指标体系中,建立风险证券组合投资决策和存在无风险证券或无风险贷款时证券组合投资决策的多目标线性规划模型．研究了有效风险证券组合集和有效证券组合集的结构和相互关系,市场证券组合以及证券均衡市场价格和投资风险分析．     

一维流体动力学半导体方程解的Lp-收敛率

文讨论了一维流体动力学半导体方程,当压强函数为p(n)=kn~r,k >0,r≥1时,我们得到了带小初值的Cauchy问题的解的存在性.利用格林函数的办法,我们还得到解的L~p-估计,即当初值是某一常状态附近的小扰动时,其相应的解也是该常状态附近的小扰动。     

一维半导体流体动力学模型的局部有界解

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。     

ON THE EXISTENCE WITH EXPONENTIAL DECAY AND THE BLOW-UP OF SOLUTIONS FOR COUPLED SYSTEMS OF SEMI-LINEAR CORNER-DEGENERATE PARABOLIC EQUATIONS WITH SINGULAR POTENTIALS

In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare′inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family.     

Ladyzhenskaya模型的非协调有限元逼近

§1.引言 Navier-Stokes方程是描述粘性不可压缩流体运动的偏微分方程,它是研究这类非线性问题的很好的数学模型。但是,当速度梯度较大时,方程的整体解是否唯一可解,这个问题尚未得到解决。为此,对于不可压缩粘性流体的定常情形,Ladyzhenskaya提出利用下面的模型来代替Navier-Stokes方程。 设Ω是R~n(n=2或3)中的有界区域,边界?ΩLipshitz连续,u是流体速度,p是     

THE EXPONENTIAL ATTRACTOR FOR THE EQUATIONS OF THERMOHYDRAULICS

In this paper, the existence of the exponential attractor for the thermohydraulics equations is proved, and the estimates of its fractal dimensions are also given,     

ON THE INITIAL VALUE PROBLEM FOR THE BIPOLAR SCHRODINGER-POISSON SYSTEM

In this paper, we prove the existence and uniqueness of global solutions in H^s(R^3) ( s∈R, s≥0) for the initial value problem of the bipolar Schrodinger-Poisson systems.     

单物种人口模型指数隐式Euler方法的振动性

本文研究了用以描述单物种人口模型的延迟Logistic方程的数值振动性.对方程应用隐式Euler方法进行求解,针对离散格式定义了指数隐式Euler方法,证明了该方法的收敛阶为1.根据线性振动性理论获得了数值解振动的充分条件.进而还对非振动数值解的性质作了讨论.最后用数值算例对理论结果进行了验证.