Global strong solutions for a class of compressible non‐Newtonian fluids with vacuum

We study a class of compressible non‐Newtonian fluids in one space dimension. We prove, by using iterative method, the global time existence and uniqueness of strong solutions provided that the initial data satisfy a compatibility condition and the initial density is small in its H¹‐norm. The main difficulty is due to the strong nonlinearity of the system and the initial vacuum. Copyright © 2010 John Wiley & Sons, Ltd.     

A linear hyperbolic system and an optimal control problem

We prove a theorem of existence, uniqueness, and continuous dependence for a linear hyperbolic system with Darboux-type conditions under assumptions on the coefficients, which are in a sense the most general possible. Moreover, an application of this result to an optimal control problem is given.     

Existence and Uniqueness of Solutions to Time-delays Stochastic Fractional Differential Equations with Non-Lipschitz Coefficients

In this paper, we consider the existence and uniqueness of solutions to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coefficients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations.     

具三个公共值的亚纯函数的唯一性

主要讨论了具有三个公共值的亚纯函数的唯一性问题，推广了仪洪勋、叶寿桢与邱淦Ｄｉ等人的有关结果。     

奇异微分系统的初值问题及其应用

利用依赖于解的奇异非线性时间变换，把奇异微分系统转换为非奇异的常微系统，建立了奇异微分系统初值问题解的(非)存在性和惟一性及多解的存在性．一阶和二阶奇异微分方程的初值问题的应用结果与Petio(2000)和Agarwal(1999)的结果相比，条件简单容易验证，且结论更详细。     

THE SIMPLE BLOCK ITERATIVE ALGORITHM OF AN EXTENDED ENTROPY MODEL AND ITS CONVERGENCE

1.ExtendedEntropyModelEntropymodelsarewidelyusedasaforecastingtechniqueinregionalplanning,see11]and[7].Theydescribeinacertainwaythemostprobablespatialinteractionandcanbeusedtoestimateorigin-destinationtripmatrices.Butthemodelsaretoosimple,soitisdifficulttomeetpracticalrequirements.HallefjordandJo..stenl2]putforwardthegeneralizationofthestandardentropymodels.Onthebasisofthisandaccordingtothedemandofthepredictionofthetripamountfortransportationplanning,wearriveatthefollowing:wherep,μandnarepo…     

Mathematical modelling of rock bolt systems I

The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties.     

Exact Controllability and Boundary Stabilization of Torsional Vibrations of an Internally Damped Flexible Space Structure

In this paper, we study the exact controllability and boundary stabilization of the torsional vibrations of a flexible space structure (such as a solar cell array) modeled by a rectangular panel, incorporating the material damping of the structure. The panel is hoisted at one end by a rigid hub and the other end is totally free. For the attachment of this hub on one side of the panel, the hub dynamics leads to a nonstandard boundary condition. To incorporate internal damping of the material, we assume Voigt-type viscoelasticity of the structure. Exact controllability theory is established using the Hilbert uniqueness method by means of a control torque applied only on the rigid hub of the panel. At the same time, uniform exponential energy decay rate is obtained directly for the solution of this problem.     

一类非经典扩散方程整体解的存在唯一性及长时间行为

本文讨论非经典扩散方程第一初边值问题整体解的存在唯一性及长时间行为，建立了一系列新的结果，较好地改进许多已有的结论．     

Multistep methods for differential algebraic equations

Multistep methods for the differential/algebraic equations (DAEs) in the form of