一类非线性算子方程的正算子解的研究

研究了算子方程X^(-1)+A(-1)+A⁺X+X^tA=Q,的正算子解问题,给出了此类非线性算子方程正算子解的范围以及正算子解存在的一些充分必要条件,并用迭代的方法得到了方程的正算子解.     

关于算子方程AX=XAX与AX=XA=XAX

用A的不变子空间作参数，给出了算子方程AX＝XAX的全部解。当A是单射或稠值域时，或者当A是正规算子时，给出了算子方程AX＝XA＝XAX的全部解。我们还给出正规算子X是算子方程AX＝XZ＝XAX的解的充分必要条件。     

非线性算子方程X~(-1)+(AXA~*)~(1/t)=Q的正算子解的研究

在无限维Hilbert空间上研究了算子方程X~(-1)+(AXA~*)~(1/t)=Q(t1)的正算子解问题.通过构造有效的迭代序列,研究了算子方程正算子解存在的充要条件,给出了该方程有正算子解时各算子范数之间的关系以及解的范围,并用迭代的方法得到了方程的正算子解.     

算子方程AX-XA*=B的正解与实正解

利用算子矩阵分块技巧和算子的广义逆,在A是幂等算子的情况下,给出了算子方程AX-XA＊=B有正解和有实正解的充要条件,并给出了正解和实正解的通式。     

随机收缩与随机集值算子方程解集的稳定性

本文应用随机收缩,建立具有随机定义域的随机集值算子方程随机解集的稳定性定理,其推论给出了随机集值算子随机不动点集的稳定性。     

关于算子方程X＋A^＊X^-tA=Q的正算子解的研究

该文研究算子方程X+A*X-tA=Q的正算子解的问题,给出了算子方程X+A*X'-tA=Q有正算子解的一些必要条件,同时也给出了该算子方程有正算子解的充分必要条件.     

Banach空间双曲型算子方程的解

Ｂａｎａｃｈ空间双曲型算子方程的解杨根科，卫淑芝（太原重型机械学院数学教研室，太原０３００２４）§１．引言考虑Ｂａｎａｃｈ空间Ｅ中双曲型算子方程解的存在性；这里，是（Ｃ０）类线性算子半群的无穷小生成元。本文研究（１）整体温和解的存在性，解决了一类常规...     

算子方程X+A~*X~(-t)A=Q的正算子解的研究

研究了算子方程X+A*X~(-t)A=Q(t>1)的正算子解问题,分别给出了算子方程X+A*X~(-t)A=Q有正算子解的一些充分条件和必要条件,并确定了解的范围,用迭代的方法得到方程的正算子解.     

一类算子方程的正算子解的研究

对算子方程X+A~*X~(-2)A=Q有正算子解的条件做了进一步的研究,得到了方程有正算子解时A,Q,X的范数、谱半径之间新的关系.并给出了算子方程X+A~*X~(-t)A=Q有正算子解的一些条件.     

K—单调算子方法及应用

本文讨论了稠定的K-单调非线性算子的扩张,在较弱的条件下得到K-单调算子方程广义解的存在性、唯一性和投影法近似可解性的结果,最后应用于不可压缩的粘性流体绕流平板的边界层计算问题,数值效果良好。     

Blowup phenomena for a new periodic nonlinearly dispersive wave equation

We first establish the local well‐posedness for a new periodic nonlinearly dispersive wave equation. We then present a precise blowup scenario and several blowup results of strong solutions to the equation. The obtained blowup results on the equation improve considerably recent results on the Camassa‐Holm equation and the rod equation (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on solutions of an equation modelling arterial deformation

The derivation of exact solutions for a partial differential equation modelling arterial deformation in large arteries is considered. Amongst other results, we show that, for any values of the parameters appearing in the equation, solutions in terms of the first Painlevé transcendent can be obtained. This is in spite of the non-integrability of the equation. We also establish a connection, via an approximation of the equation under study by the Korteweg-de Vries equation, with the second Painlevé equation. Our results thus serve to further demonstrate the wide applicability and importance of the Painlevé equations.     

一类二阶非线性变时滞微分方程的振动准则

研究二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0,对振动因子p(t)变符号的情况讨论了方程的振动性,通过两个已有引理得到了方程振动的两个充分条件.所得结论推广了原有的二阶非线性微分方程与变时滞微分方程当系数不变号时的振动性结论,完善了具变符号振动因子的二阶非线性变时滞微分方程的研究.     

Horizontal water flow in unsaturated porous media using a fractional integral method with an adaptive time step

Predicting the horizontal groundwater flow in unsaturated porous media is a challenge in many areas of science and engineering. The governing equation associated with this phenomenon is a nonlinear partial differential equation known as the Richards equation. However, the numerical results obtained using this equation can differ substantially from the experimental results. In order to overcome this difficulty, a new version of the Richards equation was proposed recently that considers a time derivative of fractional order. In this study, we present a numerical method for solving this fractional Richards equation. Our method comprises an adaptive time marching scheme that uses Picard iterations to solve the corresponding nonlinear equations. A computational code was implemented for the proposed method using the Scilab programming language. We performed numerical simulations of the anomalous diffusion of water in a white siliceous brick and showed that the numerical results were consistent with the available experimental data.     

一类梁方程正解的存在性和对参数的依赖性

应用锥不动点定理并结合Banach空间中的半序结构,研究了一类梁方程的可解性问题.不仅得到了梁方程正解的存在性结果,并且讨论了梁方程正解对参数的依赖性.注意到梁方程中含有正参数λ和L~p-可积函数,获得的结果是新的,并从本质上推广了已有文献的结果.     

The Cauchy problem for ut=Δu+|∇u|q,large-time behaviour

The nonlinear partial differential equation in the title is typified mathematically as a viscous Hamilton–Jacobi equation. It arises in the study of the growth of surfaces, and in that context is known as the generalized deterministic KPZ equation. Considering the Cauchy problem with initial data that are merely supposed to be bounded and continuous, results on the temporal decay and large-time behaviour of solutions are presented. Corresponding results for the heat equation serve as benchmarks.     

Global existence and blow-up phenomena for a periodic 2-component Camassa–Holm equation

We first establish local well-posedness for a periodic 2-component Camassa?CHolm equation. We then present two global existence results for strong solutions to the equation. We finally obtain several blow-up results and the blow-up rate of strong solutions to the equation.     

On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation

In this paper, we study the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. We first establish the local well-posedness for the weakly dissipative μ-Hunter–Saxton equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.     

完整系统三阶Lagrange方程的一种推导与讨论

从牛顿运动方程出发，推导了完整系统关于广义加速度的Lagrange方程.讨论了该方程与传统分析力学中的Lagrange方程的相容性问题.结果显示，三阶Lagrange方程可以通过对Lagrange方程求一阶时间导数得到，表明它们是相容的.因此三阶Lagrange方程提供了一种不同于传统Lagrange方程方法的求解物体运动方程的途径.     

Oscillation and other properties of linear impulsive and nonimpulsive delay equations

Many of the oscillation results for linear impulsive equations were justified by the following scheme. First, the equivalence of the oscillation of the impulsive equation and some specially constructed nonimpulsive equation was established; further, on the base of well-known results for the nonimpulsive case, the oscillation of the impulsive equation was analyzed. In the present paper, we prove the “oscillation equivalence” result for a linear impulsive equation with a distributed delay and discuss the possibility to expand this approach to the other properties of impulsive equations, for example, stability and asymptotic behavior. In addition, a linear impulsive equation of the second order is considered.