On pathwise uniqueness of stochastic evolution equations in Hilbert spaces

The pathwise uniqueness of stochastic evolution equations driven by Q-Wiener processes is mainly investigated in this article. We focus on the case that the modulus of the continuity of the coefficients is not controlled by a linear function. Additionally, we show that the corresponding diffusion process is Feller.     

Jordan李超代数的分解再论

代数A称为不可分解的,如果A不能分解成理想的直和.满足C(Lo)=C(L)={0}的Jordan李超代数L能够分解成不可分解理想的直和,这种分解在不计理想次序的前提下是唯一的.并证明了完备Jordan李超代数的一些性质.     

On a stochastic wave equation with unilateral boundary conditions

We prove the existence and uniqueness of solutions to the initial boundary value problem for a one-dimensional wave equation with unilateral boundary conditions and random noise. We also establish the existence of an invariant measure.

     

Existence and uniqueness of solutions for singular integral equation

Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem obtained is very general and complements previous known results. The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714).     

Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching ‘well posedness’ of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems.     

Existence of solutions of initial value problems for nonlinear fractional differential equations

In this paper, by using the Schauder fixed point theorem, we study the existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations and obtain some new results.     

两类K_4同胚图的色唯一性

用k4(a ,b ,c ,d ,e,f)表示k4 同胚图 ,其中a ,b ,c ,d ,e,f分别表示度为 3的顶点间的道路的长 .本文主要研究了两类k4 同胚图的色唯一性 ,同时得到了几族新的不是色唯一的k4 同胚图     

广义Tjon-Wu方程Cauchy问题强解的存在唯一性和稳态解的存在性

利用卷积的性质和schauder不动点原理等技巧,在L_(1,i)空间中证明了一类广义Tjon-Wu方程Cauchy问题强解的存在唯一性以及稳态解的存在性.     

一类弹性系统的精确L2-能控性

该文研究带有压电驱动器的Rayleigh梁系统的精确能控性.先用算子半群方法和提升结果[9]建立了Rayleigh梁方程解的正则性;再用Hilbert唯一性方法结合Diophantine逼近理论的某些结果得到了系统的精确L2-能控性.     

Partially regular solution to Landau-Lifshitz-Maxwell equations in two dimensions

The present paper is concerned with the existence, uniqueness and singularities of the Landau-Lifshitz equation coupled with Maxwell equations on Riemannian manifold in two dimensions. It is shown that there exists a weak solution which is regular with exception of at most finitely many singular points.