X-椭圆方程弱解Hlder连续性的Green函数法

应用线性X-椭圆算子的Green函数与次Laplace算子基本解的局部比较原理,建立了具有有界可测系数散度型X-椭圆方程弱解的局部H(o|¨)lder连续性.以Green函数为核函数,通过holefilling技巧得到弱解满足Morrey引理条件,从而建立正则性结果,这在某种意义下取代了经典的DeGiorgi-Moser-Nash迭代技术.     

散度型椭圆方程Holder连续性的Green函数法

文中利用散度型非线椭圆性算子的Green函数与Laplacian算子的比较性质, 建立了具有自然增长条件下的散度型非线性椭圆方程弱解的内部H\"older连续性.     

一类椭圆方程解的连续性

本文利用对应椭圆算子的Green函数的有关性质，得到了一类带奇异低阶项椭圆方程弱解的一个连续性结果。方程的形式为：Lu-vu=f，其中v属于Kato类，f∈L(n/2,1）。     

Heisenberg-Greinerp-退化椭圆算子的广义Picone恒等式及其应用

该文建立了Heisenberg-Greiner p-退化椭圆算子的广义Picone恒等式.作为应用,给出了Hardy不等式、Sturmium比较原理和主特征值的单调性结论.最后,讨论了具有奇异项的拟线性方程的弱解问题.     

自然增长下的具VMO系数拟线性椭圆组的部分正则性

设散度型拟线性系数算子关于自变量x一致满足VMO的结构条件,对于低阶项满足自然增长条件的拟线性椭圆方程组,建立了其弱解具有确切Holder指数的部分正则性.     

上下解方法在四阶非局部边值问题中的应用

考虑具有p-Laplacian算子的四阶微分方程非局部边值问题.通过构造Green函数,利用上下解方法,结合单调迭代技巧得到了四阶非局部边值问题迭代解的存在性.最后给出实例验证主要结论.     

一类非线性拋物变分不等式解的存在性

本文研究了一类基于非线性抛物算子的变分不等式问题.首先,通过拓展偏微分方程的弱解理论定义了变分不等式的弱解.其次,利用惩罚函数并结合连续方法,证明了变分不等式存在弱解.     

热盐环流方程全局弱解的存在性

该文利用T-弱连续算子理论和空间序列方法证明了热盐环流方程全局弱解的存在性.首先根据热盐环流方程的形式选择试探函数空间和解函数空间,再将方程化为抽象的算子方程,验证算子是T-弱连续的并满足对应条件,从而得到热盐环流方程全局弱解的存在性.     

二阶椭圆和抛物型偏微分方程的非线性非局部边值问题与温控系统稳定性

本文讨论了由温度控制中提出的二阶椭圆和抛物型偏微分方程的非线性非局部边值问题.通过把问题化为变分不等方程,利用单调算子理论、凸分析和非线性发展方程理论,研究了其弱解的适定性和增长估计.证明了当反馈因(辶回)路的总增益适当小的时候,系统是全局渐近稳定的.     

关于二阶退化椭圆型算子的Harnack不等式

本文研究一类二阶退化椭圆算子。在Fefferman-Phong的几何型次椭圆条件下,对于R~2上的具有实系数的二阶退化椭圆算子得到了弱解的Harnack不等式。这里的算子的退化的阶数是可以很高的,但是系数只假设是属于C~2,因此本文的证明方法与[4]的完全不一样。     

Categorical approach to modelling and to coupling of models

Solution of any engineering problem starts with a modelling process, which typically involves a choice among different kinds of models. To create a realistic model, one has to think carefully about the modelling process. Particularly in the case of coupled problems when several models are coupled together to represent a given physical phenomenon. This paper presents an approach based on the category theory that allows to describe this modelling process on a more abstract level. Using the advantages of abstract level, one can describe the coupling process in a concise way and introduce certain criteria to check consistency of a coupled model. The main idea of the proposed approach is to introduce a structure in the modelling process, which allows to see how different models interact without a precise look into them. Copyright © 2016 John Wiley & Sons, Ltd.     

升值之言该如何听

自今年6月中国暗示将松动人民币汇率以来,人民币升值幅度仅为0．4％,这大大低于华盛顿的期待,因此,中美两国的关系日益紧张起来。随着失业率的膨胀,以及选举年即将到来,美国国会再一次将人民币汇率摆上了议事日程：9月6日,华盛顿两位高官为缓和中美关系前往北京,就人民币及其他重要问题进行高峰会晤,以期达成共识。     

Correction to a proposition related to ergodicity of Markov chains

Proposition 5.5.6 (ii) in the book Markov Chains and Stochastic Stability (2nd ed, Cambridge Univ. Press, 2009) has been used in the proof of a theorem about ergodicity of Markov chains. Unfortunately, an example in this paper shows that this proposition is not always true. Thus, a correction of this proposition is provided.     

Comparison of decay of solutions to two compressible approximations to Navier-Stokes equations

In this article, we use the decay character of initial data to compare the energy decay rates of solutions to different compressible approximations to the Navier- Stokes equations.We show that the system having a nonlinear damping term has slower decay than its counterpart with an advection-like term. Moreover, me characterize a set of initial data for which the decay of the first system is driven by the difference between the full solution and the solution to the linear part, while for the second system the linear part provides the decay rate.     

From A to B to Z

Semigroup Forum - The variety generated by the Brandt semigroup $$B_2$$ can be defined within the variety generated by the semigroup $$A_2$$ by the single identity $$x^2y^2\approx y^2x^2$$ . Edmond...     

Differentiability with respect to parameters of solutions to convex programming problems

We consider a family of convex programming problems that depend on a vector parameter, characterizing those values of parameters at which solutions and associated Lagrange multipliers are Gâteaux differentiable.These results are specialized to the problem of the metric projection onto a convex set. At those points where the projection mapping is not differentiable the form of Clarke's generalized derivative of this mapping is derived.     

Convergence to steady states of solutions to nonlinear integral evolution equations

We prove that any global bounded solution of the nonlinear evolutionary integral equation $$\dot{u}(t) + \int\limits_0^t a(t-s)\mathcal{E}'(u(s))ds =f(t), \quad t >0 $$ tends to a single equilibrium state for long time (i.e., ${\mathcal{E}'(\vartheta)=0}$ where ${\vartheta= \lim_{t \rightarrow \infty} u(t)}$ on a real Hilbert space), where ${\mathcal{E}'}$ is the Fréchet derivative of a functional ${\mathcal{E}}$ , which satisfies the ?ojasiewicz?CSimon inequality near ${\vartheta}$ . The vector-valued function f and the scalar kernel a satisfy suitable conditions.     

An approach to predictive-reactive scheduling of parallel machines subject to disruptions

In this paper, a new predictive-reactive approach to a parallel machine scheduling problem in the presence of uncertain disruptions is presented. The approach developed is based on generating a predictive schedule that absorbs the effects of possible uncertain disruptions through adding idle times to the job processing times. The uncertain disruption considered is material shortage, described by the number of disruption occurrences and disruption repair period. These parameters are specified imprecisely and modelled using fuzzy sets. If the impact of a disruption is too high to be absorbed by the predictive schedule, a rescheduling action is carried out. This approach has been applied to solving a real-life scheduling problem of a pottery company.