颗粒与流体混合物模型解的一致估计

该文利用能量方法和一致的Gronwall不等式,研究了一个颗粒与流体混合物模型解关于时间的一致估计,这个关于时间的一致估计有助于我们进一步研究解的渐近行为.     

具变指数源项和强阻尼项的波动方程解的渐近稳定性

该文主要讨论下列具强阻尼项的波动方程的初边值问题u_(tt)-div(|▽u|~(p(x)-2)▽u)-△u_t=|u|~(q(x)-2)u解的渐近行为.通过构造一个新的控制函数和利用Sobolev嵌入不等式,建立了源项和能量泛函之间的定性关系.进而,利用Komornik不等式和能量估计,给出了衰减估计.最后,证明u(x,t)=0是渐近稳定的.     

具有零阶退化方程的二阶双曲型方程奇异摄动问题的一致差分格式

本文讨论了一个二阶双曲型奇异摄动问题,它的一阶导数项含有小参数ε.首先给出该问题解的能量估计及渐近解的余项估计,然后在均匀网格上构造了一个指数型拟合差分格式,最后证明了差分解在离散的能量范数意义下一致收敛于问题的精确解.     

一维粘性守恒律初边值问题粘性激波解的渐近稳定性

本文考虑一维可压缩Navier-Stokes方程有关初边值问题粘性激波解的渐近稳定性,通过L2-能量估计,证明了在小扰动情况下,粘性激波是稳定的.     

左截断右删失数据下半参数模型风险率函数估计

文章给出了右删失左截断数据半参数模型下的风险率函数估计,讨论了风险率函数估计的渐近性质,获得了这些估计的渐近正态性,对数律和重对数律.由于假定删失机制服从半参数模型下,从而知道模型的更多信息,因此对于给出参数的极大似然估计,可以改进风险率函数估计的渐近性质.也就是说,删失数据模型具有半参数的辅助信息下, 风险率函数估计的渐近方差比通常的完全非参数的估计的渐近方差更小.这说明加入了额外的信息提高了风险率函数估计的效率.     

线性模型误差方差的经验似然估计（英文）

本文应用经验似然方法得到了线性模型误差方差的一类新的估计,证明了估计的渐近分布为正态分布且渐近方差不超过常用的误差方差估计的渐近方差,同时给出了渐近方差的显式表达.     

响应变量随机缺失下的广义变系数模型的估计

在响应变量随机缺失时,利用拟似然方法给出了广义变系数模型中非参数函数系数的估计.研究了所得到的估计的渐近性质,求出了估计的渐近偏差与渐近方差,并进行模拟比较.     

论极大似然估计的Cramér渐近有效性

参数的极大似然估计(MLE)的渐近有效性是目前极大似然估计理论中的一个研究项目.但对于参数估计的渐近有效性,从不同角度出发,给出了各种不同的定义.例如,一个估计,如果具有最优渐近正态分布(BAN)性质,则称为渐近有效估计,这是文献中常见的,研究最多的.再如从分布收敛速度出发的Bahadur渐近有效性.而Cramer于     

中立型比例延迟微分系统线性θ-方法的渐近估计

本文研究了一类线性非自治中立型比例延迟微分系统线性θ-方法的渐近稳定性,并借助于泛函不等式得到了数值解的渐近估计.此渐近估计不仅比数值渐近稳定性描述得更加精确,而且还能给出非稳定情形数值解的上界估计式.数值算例验证了相关理论结果.     

强混合样本且含附加信息情形M估计和分位数估计的渐近性质（英文）

在强混合样本且含附加信息情形,本文采用经验似然方法提出了一类新的M估计和新的分位数估计.结果表明,本文提出的M估计和分位数估计具有相合性和渐近正态性,且其渐近方差比一般M估计和分位数估计的渐近方差小.     

Global existence and asymptotic dynamics in a 3D fractional chemotaxis system with singular sensitivity

In this paper, we investigate the global existence and asymptotic dynamics of solutions to a fractional singular chemotaxis system in three dimensional whole space. We deal with the new difficulties arising from fractional diffusion by using Riesz transform and Kato-Ponce’s commutator estimates appropriately, and establish the local existence of solution. Then with the help of combining the local existence and the a priori estimates, the global existence and uniqueness of solution with small initial data is derived. Moreover, we obtain the asymptotic decay rates of solution by the method of energy estimates.     

Initial layers and zero-relaxation limits of Euler–Maxwell equations

In this paper we consider zero-relaxation limits for periodic smooth solutions of Euler–Maxwell systems. For well-prepared initial data, we propose an approximate solution based on a new asymptotic expansion up to any order. For ill-prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in time intervals independent of the relaxation time and their convergence is justified by establishing uniform energy estimates.     

Time periodic solutions of compressible Navier-Stokes equations

In this paper, we study the Navier-Stokes equations with a time periodic external force in Rn. We show that a time periodic solution exists when the space dimension n?5 under some smallness assumption. The main idea is to combine the energy method and the spectral analysis for the optimal decay estimates on the linearized solution operator. With the optimal decay estimates, we prove the existence and uniqueness of time periodic solution in some suitable function space by the contraction mapping theorem. In addition, we also study the time asymptotic stability of the time periodic solution.     

Stability of stationary solutions for the non-isentropic Euler-Maxwell system in the whole space

In this paper we discuss the asymptotic stability of stationary solutions for the non-isentropic Euler-Maxwell system in R³. It is known in the authors’ previous works [17, 18, 19] that the Euler-Maxwell system verifies the decay property of the regularity-loss type. In this paper we first prove the existence and uniqueness of a small stationary solution. Then we show that the non-stationary problemhas a global solution in a neighborhood of the stationary solution under smallness condition on the initial perturbation. Moreover, we show the asymptotic convergence of the solution toward the stationary solution as time tends to infinity. The crucial point of the proof is to derive a priori estimates by using the energy method.     

On the decay of solutions to the 2D Neumann exterior problem for the wave equation

We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.     

Initial layers and zero‐relaxation limits of multidimensional Euler–Poisson equations

In this paper, we consider zero‐relaxation limits for periodic smooth solutions of the time‐dependent Euler–Poisson system. For well‐prepared initial data, we construct an approximate solution by an asymptotic expansion up to any order. For ill‐prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in a time interval independent of the relaxation time, and their convergence is justified by establishing uniform energy estimates. Copyright © 2012 John Wiley & Sons, Ltd.     

On the asymptotic exactness of error estimators for linear triangular finite elements

Summary This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution.One of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation. This estimator is equivalent to the error in the energy norm under rather general conditions. However, we show that for the asymptotic exactness, the regularity assumption on the mesh is not merely technical. While doing this, we analyze the relation between superconvergence and asymptotic exactness for some particular examples.     

The Cauchy problem of a fluid‐particle interaction model with external forces

In this paper, we consider the Cauchy problem of a fluid‐particle interaction model with external forces. We first construct the asymptotic profile of the system. The global existence and uniqueness theorem for the solution near the profile is given. Finally, optimal decay rate of the solution to the background profile is obtained by combining the decay rate analysis of a linearized equation with energy estimates for the nonlinear terms. The main method used in this paper is the energy method combining with the macro‐micro decomposition.     

Expanding solitons with non-negative curvature operator coming out of cones

We consider Ricci flow of complete Riemannian manifolds which have bounded non-negative curvature operator, non-zero asymptotic volume ratio and no boundary. We prove scale invariant estimates for these solutions. Using these estimates, we show that there is a limit solution, obtained by scaling down this solution at a fixed point in space. This limit solution is an expanding soliton coming out of the asymptotic cone at infinity.     

On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model

In this paper, we consider the vanishing viscosity limit problem for a system arising from the Keller-Segel equations in three space dimensions. First, we construct an accurate approximate solution that incorporates the effects of boundary layers. Then, we prove the structural stability of the approximate solution as the chemical diffusion coefficient tends to zero. Our approach is based on the method of matched asymptotic expansions of singular perturbation theory and the classical energy estimates.