Compressible navier-stokes equations with density-dependent viscosity, vacuum and gravitational force in the case of general pressure

This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.     

Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes

It is shown that, in the pattern recognition problem with two nonoverlapping classes, the matrices of estimates of the object closeness are described by a metric. The transition to the algebraic closure of the model of recognizing operators of finite degree corresponds to the application of a special transformation of this metric. It is proved that the minimal degree correct algorithm can be found as a polynomial of a special form. A simple criterion for testing classification implementations is obtained.     

The Marple algorithm for the autoregressive spectral estimates of the SMMW fourier transform spectroscopy data

The Marple algorthm for the autoregressive spectral estimates has been applied to the SMMW Fourier transform spectrum analysis. The experimental results have shown that this method yields AR spectra with three times higher resolution than the FFT method does. The improvements obtained from the Marple algorithm over the maximum entropy algorithm include higher resolution, less bias in the spectral peak frequency estimation and absence of observed spectral line splitting. The effects of the structure of the spectral lines and the noise on the resolution are discussed.Projects supported by National Natural Science Foundation of China     

The affine Plateau problem

In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.

     

Numerical analysis of two frictionless elastic-piezoelectric contact problems

In this work, we consider two frictionless contact problems between an elastic-piezoelectric body and an obstacle. The linear elastic-piezoelectric constitutive law is employed to model the piezoelectric material and either the Signorini condition (if the obstacle is rigid) or the normal compliance condition (if the obstacle is deformable) are used to model the contact. The variational formulations are derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a discrete scheme is introduced based on the finite element method to approximate the spatial variable. Error estimates are derived on the approximate solutions and, as a consequence, the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, some two-dimensional examples are presented to demonstrate the performance of the algorithm.     

热传导型半导体瞬态问题的特征有限体积方法及分析

在这篇文章中,将特征线方法与有限体积方法相结合,构造了热传导型半导体瞬态问题的全离散特征有限体积方法(CFVM).在一般的条件下进行理论分析,得到了次优阶L2误差估计结果.     

Boltzmann-Poisson系统解的动量及能量估计

In this paper, the properties of the solutions of Boltzmann-Poisson system in three dimensions are considered. The estimates of the energies (the kinetic and the potential energies) and the γ-th moments with γ∈[2,3) are obtained. The latter answers an open problem.     

Exponential square integrability for non-tangential limits of certain smooth functions

Under the assumption of the boundedness of certain operator (resembling Lusin's area function) of a smooth function u that satisfies certain interior regularity property, we prove the exponential square integrability of the boundary values of u.     

Volume growth and heat kernel estimates for the continuum random tree

In this article, we prove global and local (point-wise) volume and heat kernel bounds for the continuum random tree. We demonstrate that there are almost–surely logarithmic global fluctuations and log–logarithmic local fluctuations in the volume of balls of radius r about the leading order polynomial term as r → 0. We also show that the on-diagonal part of the heat kernel exhibits corresponding global and local fluctuations as t → 0 almost–surely. Finally, we prove that this quenched (almost–sure) behaviour contrasts with the local annealed (averaged over all realisations of the tree) volume and heat kernel behaviour, which is smooth.      

Fourier series and integral equation method for the exterior Stokes problem

The exterior Stokes problem between two parallel planes that are separated by a prismatic cylinder is extended to the interior of the prism by requiring the continuity of the velocity across the lateral faces. The well‐posedness of the exterior–interior problem is proved in suitable weighted Sobolev spaces. The solution is represented by Fourier series in the z‐variable. The Fourier coefficients, solutions of auxiliary two‐dimensional exterior–interior problems, are analyzed by viewing them as boundary integral equations of potential theory and global regularity of the densities, is established in weighted Sobolev spaces of traces. A boundary element method, with suitably refined mesh size, is implemented for the numerical treatment of the Fourier coefficients. This provides optimal convergent semi‐ and fully‐discrete spectral methods of Fourier–Galerkin type. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008