对流扩散方程特征线双线性元的一致估计

利用双线性元的积分恒等式,给出了二维非定常对流占优扩散方程的特征线有限元解和真解的一致误差估计,并利用插值后处理算子给出了有限元解梯度的一致超收敛估计,即上述误差与ε无关,而仅与右端f和初值u_0有关.     

Gumbel分布的简单贝叶斯估计

在实际应用中,两参数Gumbel分布的贝叶斯估计往往需要预先知道Gumbel参数的二维联合先验分布。由于获取先验分布的主观性和统计推断的复杂性,目前有关Gumbel分布贝叶斯估计理论及其性质的讨论还比较少,更不要说获得较为简单的Gumbel分布的贝叶斯估计。本文基于Kaminskiy和Vasiliy提出的简单贝叶斯估计过程,利用可靠度函数估计的区间形式表示先验信息,从而得到两个参数Gumbel分布的简单贝叶斯估计。基于此先验信息,该估计过程构造了Gumbel参数的连续联合先验分布,给出了在给定任意时点的可靠度(或累积密度)及其标准差的后验估计,为可靠性与风险评估中简单快速的使用贝叶斯估计刻画极端事件提供了可能.     

粘弹性波动方程的H~1-Galerkin混合有限元方法误差估计(英文)

H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.     

Weighted Sobolev L2 estimates for a class of Fourier integral operators

In this paper we develop elements of the global calculus of Fourier integral operators in ${{\mathbb R}^n}$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L² estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of weighted estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions.     

Improved inhomogeneous Strichartz estimates for the Schrödinger equation

We study inhomogeneous Strichartz estimates for the Schrödinger equation for dimension n?3. Using a frequency localization, we obtain some improved range of Strichartz estimates for the solution of inhomogeneous Schrödinger equation except dimension n=3.     

Concerning the Strauss conjecture on asymptotically Euclidean manifolds

In this paper we verify the Strauss conjecture for semilinear wave equations on asymptotically Euclidean manifolds when n=3,4. We also give an almost sharp lifespan for the subcritical case 2?p<pc when n=3. The main ingredients include a Keel-Smith-Sogge type estimate with 0<μ<1/2 and weighted Strichartz estimates of order two.     

Invariant elliptic estimates

In this paper, we revisit elliptic estimates invariant under domain expansion. We improve the invariant elliptic estimates in the previous paper [Y. Cho, T. Ozawa, Y. Shim, Calc. Var. PDE 34 (2009) 321-339] via gradient estimate and discuss an application to the Lamé system.     

The Nonlinear Schr¨odinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type

The primary goal of this paper is to present a comprehensive study of the nonlinear Schr?dinger equations with combined nonlinearities of the power-type and Hartree-type. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schr?dinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.     

Heteroscedastic normal-exponential mixture models: Bayesian and classical approaches

In this paper, we introduce a Bayesian analysis for mixture of distributions belonging to the exponential family. As a special case we consider a mixture of normal exponential distributions including joint modeling of the mean and variance. We also consider joint modeling of the mean and variance heterogeneity. Markov Chain Monte Carlo (MCMC) methods are used to obtain the posterior summaries of interest. We also introduce and apply an EM algorithm, where the maximization is obtained applying the Fisher scoring algorithm. Finally, we also include analysis of real data sets to illustrate the proposed methodology.     

A characteristic-mixed finite element method for time-dependent convection-diffusion optimal control problem

In this paper, we examine the method of characteristic-mixed finite element for the approximation of convex optimal control problem governed by time-dependent convection-diffusion equations with control constraints. For the discretization of the state equation, the characteristic finite element is used for the approximation of the material derivative term (i.e., the time derivative term plus the convection term), and the lowest-order Raviart-Thomas mixed element is applied for the approximation of the diffusion term. We derive some a priori error estimates for both the state and control approximations.