A finite difference scheme for the nonlinear time-fractional partial integro-differential equation

In this paper, a finite difference scheme is proposed for solving the nonlinear time-fractional integro-differential equation. This model involves two nonlocal terms in time, ie, a Caputo time-fractional derivative and an integral term with memory. The existence of numerical solutions is shown by the Leray-Schauder theorem. And we obtain the discrete L₂ stability and convergence with second order in time and space by the discrete energy method. Then the uniqueness of numerical solutions is derived. Moreover, an iterative algorithm is designed for solving the derived nonlinear system. Numerical examples are presented to validate the theoretical findings and the efficiency of the proposed algorithm.     

UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.     

非线性分数阶反应扩散方程组的间断时空有限元方法

利用时间间断空间连续的时空有限元方法构造了空间分数阶反应扩散方程组的可以逐时间层求解的全离散格式.在时间离散区间上,采用Radau积分公式,将插值理论与有限元理论相结合,给出了全离散格式解的存在唯一性结果,并证明了所给格式是无条件稳定的,进而详细给出最优阶L~∞(L~2)模误差估计过程.最后用数值算例验证了理论分析的正确性.     

New models of Cahn-Hilliard-Gurtin equations

In this article, we further generalize the models of Cahn-Hilliard equations proposed by Gurtin and based on a balance law for microforces. We then study the existence and uniqueness of solutions and the boundedness of the order parameter.Received: 26 May 2003, Accepted: 29 August 2003, Published online: 3 February 2004PACS: 02.30.Jr, 64.75. + g Correspondence to: M. Efendiev     

Hyperbolic boundary value problem with equivalued surface on a domain with thin layer

This paper deals with a kind of hyperbolic boundary value problems with equivalued surface on a domain with thin layer. Existence and uniqueness of solutions are given, and the limit behavior of solutions is studied in this paper. Project partially supported by NSFC (No:10401009) and NCET of China (No:060275).     

SOlvaBILITY OF HIGHER INDEX TIME-VARYING LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

1 IntroductionNormal differential-algebraic equatiOns (DAEs) are siugular ordiuary differe11tial equations(ODEs)f(x,(t),x(f),f) = 0, (1.1)wllere the partial Jacobian f;(y, x, f) E L(n") is everywliere singular but has constant rank.Such systelns are of special interest in view of various applicatiOns, e.g. electrical networks,constrailled lllecl1anica1 systenis of rigid bodies, coutrol theory, singular perturbatio11 and dis-cretization of partia1 differential equations, etc. (cf [1,2,3]).I…     

亚纯函数及其n阶导数权分担两个值

研究亚纯函数及其n阶导数权分担两个值的唯一性问题.得到了：如果两个非常数亚纯函数f,g分担（∞,∞）,f（n）与g（n）分担（1,0）,n（≥0）为一整数,且满足C0：=（4n＋6）λ＋δn＋1（0,f）＋δn＋1（0,g）＋δn＋2（0,f）＋δn＋2（0,g）＋δn（0,f）〉4n＋10,其中λ=max{min{Θ（∞,f）,Θ（0,f）},min{Θ（∞,g）,Θ（0,g）}},那么f（n）·g（n）≡1,或者f≡g.该结果改进了前人的有关定理.     

An Explicit Solution of a Parabolic Equation with Nonlocal Boundary Conditions

We consider a parabolic differential equation with nonlocal boundary conditions. We find an explicit solution of the problem and prove the uniqueness of the solution. Analysis of the explicit solution reveals that it has three physically different linear components. The first component is of standing wave type, and the other two are of right- and left-going wave types, respectively. The speed of propagation of the heat waves depends on constants present in nonlocal boundary conditions. We give examples of right-going heat waves that have constant energy. This work was partially supported by Lithuanian State Science and Studies Foundation grant No. C-07/2003. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 315–332, July–September, 2005.     

两类新的匹配唯一性图族

本文研究了具有度序列(13,2S-4,3)的图的匹配唯一性,给出了T(1,4,n)∪(s∪i=0Cpi)(n 4)与T(1,5,n)∪(s∪i=0Cpi)(n 5)及其补图匹配唯一的充要条件.     

半线性方程周期边值问题

本文利用整体反函数理论，研究了半线性周期边值问题，给出存在唯一性的充分条件，推广和改进了现有的结果。