一类非自治发展方程的一致吸引子

本文研究一类非自治发展方程的渐近行为,运用算子分解及分析技巧得到了系统解的渐近正则性,由此证明一致吸引子的存在性、正则性及其结构.其中非线性项满足临界指数增长,时间依赖的外力项仅假设是平移有界而不是平移紧的.     

非线性发展方程的小模板简化Padé格式

在有理逼近的紧致格式的理论基础上,采用特别的统一的Pad啨逼近形式,构造了针对高阶非线性发展方程的、简单小模板的差商格式·　不仅保持了格式的四阶精度,而且还可以采用追赶法求解得到的3对角矩阵,或者采用三阶Runge_Kutta法直接求解积分·　计算效果通过多种算例表明是十分令人满意的·　相对于其他差分格式,此方法具有模板较小而精度保持四阶的优点·     

一类非自治发展方程一致吸引子的存在性

本文主要讨论一类非线性发展方程整体强解的长时间行为,利用文献[3]的方法,我们获得了整体强解对应的解过程族的一致耗散性,然后,通过验证一致(关于σ∈Σ)ω-极限紧,得到了系统的一致吸引子的存在性,其中非线性项满足临界指数增长条件.     

Existence of Mild Solutions for a Class of Fractional Non-autonomous Evolution Equations with Delay

In this paper, we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo’s fractional derivatives. By using the measure of noncompactness, β-resolvent family, fixed point theorems and Banach contraction mapping principle, we improve and generalizes some related results on this topic. At last, we give an example to illustrate the application of the main results of this paper.     

非自治退化抛物-双曲方程的柯西问题

非自治退化抛物-双曲型方程可以描述许多自然现象.主要研究这类方程的柯西问题,建立了动力学公式,在对流函数、扩散函数适当光滑性的基础上,证明了该问题动力学解的存在唯一性.     

倒向随机方程期权定价模型的一类随机算法

期权定价问题可以转化为对倒向随机微分方程的求解,进而转化为对相应抛物型偏微分方程的求解.为了求解与倒向随机微分方程相应的二阶拟线性抛物型微分方程初值问题,引入一类新的随机算法-分层方法取代传统的确定性数值算法.这种数值方法理论上是通过弱显式欧拉法,离散其相应随机系统解的概率表示而得到.该随机算法的收敛性在文中得到证明,其稳定性是自然的.并构造了易于数值实现的基于插值的算法,实证研究说明这种算法能很好地提供期权定价模型的数值模拟.     

On Linear Implicit Non-autonomous Systems of Difference Equations

This paper deals with the solvability of initial-value problems (IVPs) and multipoint boundary-value problems (MPBVPs) for linear implicit non-autonomous systems of difference equations.     

Invariant Foliations and Decoupling of Non-autonomous Difference Equations

In this paper, we continue a previous study of the geometric properties of a certain prototype system of nonautonomous difference equations. In fact, we show that by means of the fundamental theorem on the existence of invariant fiber bundles two foliations of the extended state space can be found. This detailed information about the geometric structure of the underlying system is then used to construct transformations establishing the topological equivalence between a given coupled and a completely uncoupled system.     

Slow and Fast Variables in Non-autonomous Difference Equations

In this paper we present an existence and smoothness result for center-like invariant manifolds of non-autonomous difference equations with slow and fast state-space variables. This result can be seen as a first step to obtain Fenichel's geometric theory for difference equations. Hereby, our basic tool is an abstract integral manifold theorem.     

Random Partitions by Semigroup Methods

P of all partitions of {1,2,3,...}, or rather its distribution. There is a natural compact metrizable topology on P taking care of measurability questions. With respect to the maximum operation P becomes an abelian semigroup, and our first theorem characterizes random partitions as normalized positive definite functions on the subsemigroup of partitions "with finite support". We then present a new proof of Kingman's theorem stating that the exchangeable random partitions form a simplex whose extreme points are the so-called "paint-box distributions". An interesting moment problem which is still open arises in this connection.     

Pullback Attractors for a 3D Non-autonomous Navier-Stokes-Voight Equations

Acta Mathematicae Applicatae Sinica, English Series - This paper is concerned with the existence of pullback attractors for the three dimensional non-autonomous Navier-Stokes-Voight equations for...     

A Characteristic Equation for Non-autonomous Partial Functional Differential Equations

We characterize the exponential dichotomy of non-autonomous partial functional differential equations by means of a spectral condition extending known characteristic equations for the autonomous or time-periodic case. From this we deduce robustness results. We further study the almost periodicity of solutions to the inhomogeneous equation. Our approach is based on the spectral theory of evolution semigroups.     

Sufficient Conditions for the Oscillation of Non-autonomous Difference Equations

Abstract In this paper, we obtain sufficient conditions for the oscillation of the non-autonomous differenceequations x(n 1)-x(n) sum from i=1 to m p_i(n)x(n-r_i(n))=0,which are the discrete analog of the delay differential equations considered in[1].     

时滞依赖状态的非自治多值偏积分微分方程

利用预解算子理论结合Leray-Schauder型多值映射不动点定理,在公理化定义的相空间上,得到了一类时滞依赖状态的非自治多值一阶偏积分微分方程适度解的存在性.     

Fourth Order Conservative Exponential Methods for Linear Evolution Equations

A few numerical methods for linear evolution equations are developed and analyzed in this paper. These fourth order exponential methods reproduce the exact solutions for equations with time-independent evolution operators. For highly oscillatory problems with evolution operators that vary slowly in time, these methods are often more efficient than the traditional methods, since large step sizes can be used. The methods developed in this paper are also conservative for equations such as the Schrödinger equation, where the evolution operator is skew-selfadjoint.     

A Mathod to Solve Systems of Fuzzy Linear Equations

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅｗｉｌｌｃｏｎｃｅｒｎｗｉｔｈｓｏｌｖｉｎｇｔｈｅｓｙｓｔｅｍｓｏｆｆｕｚｚｙｌｉｎｅａｒｅｑｕａｔｉｏｎｓＡｘ＝ｂｆｏｒｘ，ｗｈｅｒｅＡｉｓａｍａｔｒｉｘｏｆｆｕｚｚｙｎｕｍｂｅｒｓ；ｘａｎｄｂａｒｅｖｅｃｔｏｒｓｏｆｆｕｚｚｙｎｕｍｂｅｒｓ．Ｉｎ［２］，ｕｓｉｎｇｔｈｅｎｅｗｓｏｌｕｔｉｏｎｃｏｎｃｅｐｔ，ｓｉｘｎｅｗｓｏｌｕｔｉｏｎｓａｒｅｄｅｆｉｎｅｄ．Ｔｈｉｓｄｉｓｃｕｓｓｉｏｎｗａｓｒｅｓｔｒｉｃｔｅｄｔｏｓｑ…     

A Numerical Method to Solve Higher-Order Fractional Differential Equations

Mediterranean Journal of Mathematics - In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present...     

一道常微分方程例题的多种解法

针对同济大学应用数学系所编《微积分》教材中一道求一阶常微分方程特解的例题,在原有幂级数解法之外,给出另三种解法,即Lyapunov人工小参数法,Adomain分解法和δ展开法.