Existence of global strong solution to the micropolar fluid system in a bounded domain

In this paper we are concerned with the initial boundary value problem of the micropolar fluid system in a three dimensional bounded domain. We study the resolvent problem of the linearized equations and prove the generation of analytic semigroup and its time decay estimates. In particular, L^p–L^q type estimates are obtained. By use of the L^p–L^q estimates for the semigroup, we prove the existence theorem of global in time solution to the original nonlinear problem for small initial data. Furthermore, we study the magneto‐micropolar fluid system in the final section. Copyright © 2005 John Wiley & Sons, Ltd.     

Matrix extensions and eigenvalue completions, the generic case

In this paper we provide new necessary and sufficient conditions for the so-called eigenvalue completion problem.

     

Global Smooth Solutions of the Equations of a Viscous,Heat - Conducting,One - Dimensional Gas with Density - Dependent Viscosity

We consider initial boundary value problems for the equations of the one-dimensional motion of a viscous, heat-conducting gas with density-dependent viscosity that decreases (to zero) with decreasing density. We prove that if the viscosity does not decrease to zero too rapidly, then smooth solutions exist globally in time.     

超线性奇异边值问题解的全局结构

本文讨论一类具有奇异性的超线性边值问题.我们证明,解集存在无界连通分支.作为推论,我们在一定程度上改进了文[1]的主要结果,去掉了其主要条件.     

Vacations in GI X/M Y/1 systems and Riemann boundary value problems

We consider systems of GI/M/1 type with bulk arrivals, bulk service and exponential server vacations. The generating functions of the steady-state probabilities of the embedded Markov chain are found in terms of Riemann boundary value problems, a necessary and sufficient condition of ergodicity is proved. Explicit formulas are obtained for the case where the generating function of the arrival group size is rational. Resonance between the vacation rate and the system is studied. Complete formulas are given for the cases of single and geometric arrivals. This revised version was published online in June 2006 with corrections to the Cover Date.     

Formulation,Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems

In this paper, we present a unified treatment and analysis of a dynamic traffic network model with elastic demands formulated and studied as a projected dynamical system. We propose a travel route choice adjustment process that satisfies the projected dynamical system. Under certain conditions, stability and asymptotical stability of the equilibrium patterns are then derived. Finally, two discrete-time algorithms, the Euler method and the Heun method, are proposed for the computation of the solutions, and convergence results established. The convergence results depend crucially on stability analysis. The performance of the algorithms is then illustrated on several transportation networks.     

弹性力学的Lagrange形式：用Routh方法建立弹性有限变形问题的基本方程

将弹性有限变形问题纳入Lagrange力学的理论体系中，并用经典力学中业已存在的Routh方法构建了有限变形平面应变问题和有限变形平面应力问题的基本微分方程，讨论了有限变形大挠度问题vonkarman方程中存在的矛盾进而提出了两种改进方案．     

拟线性常微分方程在半无限区间的边值问题

Existence of positive solution is established for boundary value problems of non-singular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the nonlinear alternative of Leray-Schauder method.     

Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type

In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.     

CALCULUS OF VARIATIONS WITH DIRICHLET BOUNDARY VALUE PROBLEM FOR PERTURBED SECOND-ORDER DIFFERENTIAL EQUATIONS ON A HALF-LINE

Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.