浅谈解的存在唯一性定理在《偏微分方程数值解》中的应用

从一个新的角度讨论常微分方程中解的存在唯一性定理在偏微分方程数值解法中的重要应用。给出一类伪双曲型偏微分方程的新的分裂混合有限元数值格式,将该格式转化成常微分方程系统,利用解的存在唯一性定理证明该系统是存在唯一解的。通过简短的讨论、概述明确解的存在唯一定理在偏微分方程数值解中的应用方法．并希望能够在教学科研未来的发展中有新的观念。     

Anti-periodic fractional boundary value problems

We study a class of anti-periodic boundary value problems of fractional differential equations. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results.     

Finite difference discretization of the extended Fisher-Kolmogorov equation in two dimensions

Approximate solutions are considered for the extended Fisher-Kolmogorov (EFK) equation in two space dimension with Dirichlet boundary conditions by a Crank-Nicolson type finite difference scheme. A priori bounds are proved using Lyapunov functional. Further, existence, uniqueness and convergence of difference solutions with order O(h²+k²) in the L^∞-norm are proved. Numerical results are also given in order to check the properties of analytical solutions.     

Existence of optimal controls for systems driven by FBSDEs

We prove the existence of optimal relaxed controls as well as strict optimal controls for systems governed by non linear forward-backward stochastic differential equations (FBSDEs). Our approach is based on weak convergence techniques for the associated FBSDEs in the Jakubowski S-topology and a suitable Skorokhod representation theorem.     

一类可修复系统的解的存在唯一性

对于一类具有人为故障率,修复率时间任意分布的可修复系统的数学模型,利用泛函理论将此系统转换为Banach空间下的第二型Volterra微分-积分方程,利用泛函分析初等方法得到系统解的存在唯一性证明,并同时得到系统解的形式。     

临界总原理在非线性波动方程中的应用

研究了带有Dirichlet边界条件的波动方程，并利用临界总原理证明了其解的多重性，从而推广了参考文献[3]的结果。     

On the existence,uniqueness and nature of Carathéodory and Filippov solutions for bimodal piecewise affine dynamical systems

In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in the context of general differential inclusions are quite restrictive when applied to bimodal piecewise affine systems. Later, we present a set of necessary and sufficient conditions for uniqueness of Filippov solutions for bimodal piecewise affine systems. We also study the so-called Zeno behavior (possibility of infinitely many switchings within a finite time interval) for Filippov solutions.     

低渗透非达西气体渗流模型及计算方法

在一系列假定条件下,建立了一个低渗透非达西气体渗流的非线性移动边界偏微分方程数学模型,在理论上论证模型解的存在唯一性基础上,用对数网格对求解区域进行剖分,建立显式预测隐式校正格式,进而讨论模型的算法。此模型和算法具有一定的应用价值。     

“有”“无”之间 仁恒观棠、棠北社区设计

文章表达建筑师面对当下中国建筑设计中追求强烈视觉效果的倾向,思考用更多富含传统建筑意境的空间处理手法来表达东方哲学中对意境的追求。通过苏州仁恒观棠社区、棠北社区的设计实践,建筑师对建筑布局、建筑院落空间、建筑街巷空间以及材料进行积极尝试,最终用建筑留白、摹画自然、自我消隐的方式诠释了传统建筑意境,用＂无＂表达了更多的＂有＂。