半无界空间上的拟线性抛物型方程解的Blow—up现象

本文研究了拟线性抛物型方程的初边值问题在无界区域D上的全局解存在性问题和局部解的Blow-up问题．利用上、下解方法，并借助Green函数，给出了问题（I）全局解的存在性条件，也给出了局部解发生Blow－up现象的条件     

线性流形上D对称矩阵反问题的最小二乘解

本研究了线性流形上D对称矩阵反问的最小二乘解及其逼近问题，给出了最小二乘解的一般表达式，并就该问题的特殊情况－矩阵反问题，获得了有解的充分必要条件，并在有解的条件下得到了解的一段表达式。     

非Lévy型正交各向异性开口圆柱壳屈曲问题的辛叠加解析解

该文基于笔者提出的辛叠加方法得到了经典解法难以直接获得的典型非Lévy型正交各向异性开口圆柱壳屈曲问题的解析解.首先，基于Donnell薄壳理论建立了正交各向异性开口圆柱壳屈曲问题的Hamilton体系控制方程，然后将非Lévy型边界下的原问题拆分为两个子问题，在Hamilton体系下利用分离变量和辛本征展开等数学手段对子问题进行求解，最后基于原问题边界条件，通过子问题解的叠加求得原问题的解析解.数值算例表明，辛叠加解析解与有限元数值解结果吻合良好.同时，定量研究了长度和厚度等参数对屈曲载荷的影响.相比于半逆解法等传统解析方法，辛叠加方法基于严格的数学推导，无需假定解的形式，可以获得更多类似问题的解析解.     

线性流形上反对称正交对称矩阵反问题的最小二乘解

该文讨论了线性流形上矩阵方程AX=B反对称正交对称反问题的最小二乘解及其最佳逼近问题．给出了最小二乘问题解集合的表达式，得到了给定矩阵的最佳逼近问题的解，最后给出计算任意矩阵的最佳逼近解的数值方法及算例．     

一类非线性奇摄动方程的激波问题

利用奇摄动理论和匹配原理，讨论了一类非线性奇摄动方程的激波问题．首先，构造了原问题的外部解和内层解．其次，研究了当激波在区间的边界附近和内部的激波解．最后，得出了与边界条件相对应的激波位置及解的表达式．     

一类网络模型问题的几步算法

本文讨论了线性规划问题：≥０，ｔ＝１，２，…，ｎ）解的性质。此规划问题可来源于网络流模型，也可来源于库存模型等。通过对该问题解的基本特征进行描述，得到了最多ｎ步即可得到精确解的快速求解方法。     

非线性年龄结构种群的平衡解

讨论一类总数依赖非线性年龄结构种群模型的动力特性，给出了系统的一个等价问题，并讨论了系统的平衡解和非平衡解，得到了平衡解和非平衡解存在的充要条件。     

三维种群生态动力系统的参数识别

研究具有反应一扩散现象的三维种群生态动力系统的参数识别问题，依该系统正问题解的性质，建立了参数识别的数学模型；论证了系统正问题解关于待识别参数的连续依赖性与参数识别问题最优解的存在性。     

运输问题求解的一种网络算法

本着重探讨了在网络图上求运输问题的初始解的方法，并指出在求解受时间约束的运输问题时得到的初始解，在很大程度就是该问题的最优解，通过实例说明了该算法。     

二阶非线性椭圆偏微分方程Dirichlet问题的粘性解

研究了一类二阶非线性椭圆偏微分方程Dirichlet问题粘性解的存在性与唯一性。首先建立粘性解的比较定理，确保了解的唯一性，然后运用Perron方法构造出解。从而解决了这类问题的粘性解的存在性与唯一性。     

Nonlinear perturbations of a ‐Laplacian equation with critical growth in

We prove the existence of solution for a class of ‐Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.     

Is Landau Damping Possible in a Shear Fluid Flow?

Asymptotic analysis for small long‐wave perturbations of a given stationary shear flow of an ideal fluid with free boundary as is performed. It is shown that small disturbances of the flow are attracted to periodic solution in the case where the governing equations are hyperbolic on the main shear flow solution. A class of shear flows for which Landau damping is realizable, is described. Analytical results obtained are validated by numerical calculations.     

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non‐negative solution couples (u,v) of with positive parameters χ and λ, where the spatial domain is the interval (0,1). This system appears as a limit case of a model for morphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75 , 2007). Under suitable boundary conditions, modeling the presence of a morphogen source at x = 0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover, we prove the convergence of the solution to the unique steady state provided that χ is small and λ is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements. Copyright © 2012 John Wiley & Sons, Ltd.     

A new family of discontinuous finite element methods for elliptic problems in the whole space

We investigate a new hybrid method we call the discontinuous Galerkin‐inverted finite element method (DGIFEM) to approximate the solution of elliptic problems in , especially when the growth or the decay of the solution is very slow. On the basis of both the discontinuous Galerkin discretization and the inverted finite element method, the DGIFEM keeps part of the domain bounded and maps the other infinite extent into a bounded region via a suitable polygonal inversion. The numerical solution is then constructed in an appropriate subspace of weighted Sobolev spaces, where the weights allow the control of the growth or the decay of functions at infinity. A careful study of the convergence of the DGIFEM is carried out and shows that the optimal order of convergence can always be reached. Finally, some numerical results are given as illustration of the good performance of the proposed method.     

Rn上一类拟线性椭圆方程正解的存在性

本文讨论了Rn 上如下一类带临界增长的拟线性椭圆方程正解的存在性 :-div(｜ u｜p- 2 u) -axn｜ u｜p- 2 u xn +｜u｜p- 2u=up - 1 ,xn ≠ 0 ,x∈Rn.这里 ,1

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使用Hodge分解得到了下列结果 :若f∈W1,n(1-ε)0 (Ω ,Rn) ,n>33为Beltrami方程组 (1 )的广义解 ,并且ε<14× 1 0 4lognabn/2 ,这里a与b来自 (2 ) ,则f=0 ,a .e.Ω .     

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Sign‐changing bubble for Neumann problem with critical nonlinearity on the boundary

The main purpose of this paper is to construct sign‐changing solution for the following Neumann problem: where n≥3 and K is a bounded and continuous function on , which concentrate around two critical points satisfying some conditions. Copyright © 2016 John Wiley & Sons, Ltd.