A new model for electrostatic MEMS with two free boundaries

A moving boundary problem with two free boundaries modeling a two-dimensional idealized MEMS device with pull-in instability is discussed. We use a fixed point argument to show that the model possesses stationary solutions for small source voltages. We also give a rigorous evidence that solutions of the model converge towards solutions of the associated small aspect ratio equation in the vanishing aspect ratio limit.     

The residual velocity method applied to a steady free boundary-value problem of vector Laplacian type

We consider a free boundary-value problem based on a simplifiedmodel of two-phase flow in porous media. The model has two independentvariables on each side of the free interface. At the interfaceat steady state, five mixed Dirichlet and Neumann conditionsare given. The movement of the interface in time-dependent situationscan be reduced to a normal motion proportional to the residualin one of the steady-state interface conditions (the ellipticinterior problems and the other interface conditions are satisfiedat each time). Following previous work, we consider the useof other residuals for the normal velocity that have superiornumerical properties. The well-posedness criteria for this vectorexample are particularly clear. The advantages of the correctlychosen, non-physical residual velocities are demonstrated innumerical computations. Although the finite-difference implementationin this work is not applicable to general problems, it has superiorperformance to previous implementations.     

具斑块迁移的病毒模型的稳定性分析

研究了一类未感染细胞斑在两斑块间迁移的病毒模型.获得了无病平衡点全局稳定性以及地方病平衡点稳定性的充分条件.研究结果表明阈值R <1且感染细胞生成病毒的速度相对小而病毒细胞死亡率足够大时,病毒趋于灭绝;而阈值R> 1且感染细胞生成病毒的速度相对大而病毒细胞死亡率足够小时,病毒持续流行.     

Well-posedness and stability for an elliptic-parabolic free boundary problem modeling the growth of multi-layer tumors

In this paper we study a free boundary problem modeling the growth of multi-layer tumors. This free boundary problem contains one parabolic equation and one elliptic equation, defined on an unbounded domain in R2 of the form 0 〈 y 〈p（x,t）, where p（x,t） is an unknown function. Unlike previous works on this tumor model where unknown functions are assumed to be periodic and only elliptic equations are evolved in the model, in this paper we consider the case where unknown functions are not periodic functions and both elliptic and parabolic equations appear in the model. It turns out that this problem is more difficult to analyze rigorously. We first prove that this problem is locally well-posed in little H61der spaces. Next we investigate asymptotic behavior of the solution. By using the principle of linearized stability, we prove that if the surface tension coefficient y is larger than a threshold value y〉0, then the unique flat equilibrium is asymptotically stable provided that the constant c representing the ratio between the nutrient diffusion time and the tumor-cell doubling time is sufficiently small.     

关于扰动微分方程零解稳定性若干定理的改进

本文运用Ляиунов第二方法研究扰动微分方程零解稳定性，分别研讨了所给扰动微分方程的局部稳定性、全局渐近稳定性以及全局一致渐近稳定性问题，得到若干定理，这些结果在一定条件下改进了文[1]的相应结果，运用更加广泛．     

Bourgain空间X~(s,b)及其在KdV型方程中的应用(英文)

本文总结了使用Bourgain空间技术研究KdV型方程初值问题的局部适定性和整体适定性方面所取得的结果.     

Asymptotic behavior of solutions of a free boundary problem modeling multi-layer tumor growth in presence of inhibitor

In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed in little Hölder spaces. Next we investigate asymptotic behavior of the solution. By computing the spectrum of the linearized problem and using the linearized stability theorem, we give the rigorous analysis of stability and instability of all stationary flat solutions under the non-flat perturbations. The method used in proving these results is first to reduce the free boundary problem to a differential equation in a Banach space, and next use the abstract well-posedness and geometric theory for parabolic differential equations in Banach spaces to make the analysis.     

Global well-posedness of the Benjamin-Ono equation in low-regularity spaces

We prove that the Benjamin-Ono initial-value problem is globally well-posed in the Banach spaces , , of real-valued Sobolev functions.

     

关于广义Benjamin－Ono方程的整体适定性

对Ｋ＞α＋３／２的广义Ｂｅｎｊａｍｉｎ－Ｏｎｏ方程，证明了当初值为小初值时相应的非线性初值问题的整体解的存在性以及唯一性．还得到了该整体在Ｌ２的意义下的渐近估计．     

一个相互干扰的食植系统的定性分析

本文运用微分方程定性理论讨论了一个相互干扰的食植系统(2),获得了该系统在J(r_2+η1/Kδ~(1/2)) <1时,极限环存在唯一以及在J(r_2+η1/Kδ~(1/2)≥1时;正平衡点全局渐近稳定。     

A note on local stability and the m-M theorem

We prove a lemma that gives global asymptotic stability of an equilibrium under appropriate hypotheses. This lemma may be used to strengthen the consequences of the m-M theorem without additional hypotheses.     

具有桥梁人群的HIV模型的研究

研究了具有桥梁人群(从事性服务的女性静脉吸毒者)的艾滋病模型.在桥梁人群内部建立一个DI模型.通过定性分析,证明了各类平衡点的稳定性,从而判断艾滋病流行与否.     

具有桥梁人群的HIV模型的持续生存

给出了一致持续性的一些概念及基本理论,建立了具有桥梁人群的H IV模型.利用所给结论研究了具有桥梁人群的H IV模型的一致持续性,从而说明艾滋病会流行起来.     

Well-posedness of general nonlocal nonhomogeneous boundary value problems for pseudodifferential equations with partial derivatives

In the article we study the questions of well-posedness of general nonlocal boundary value problems for pseudodifferential equations in the Besov-type limit spaces.     

一类高阶时滞差分方程的有界持久性与全局渐近稳定性

获得一类高阶时滞差分方程解的有界持久性和全局渐近稳定性的充分条件;所得结果部分地解决了G.Ladas的2个公开问题,推广了一些已知结果。