一类拟线性Robin问题的激波解

研究了一类Robin两点边值问题. 在适当的假设下, 利用伸长变量, 在区间内点附近构造问题解的激波层校正项. 再利用微分不等式理论, 证明了原边值问题解的存在性、一致有效性和渐近性态.     

一类拟线性边值问题的激波解

本文研究了一类拟线性边值问题的激波解，在适当的条件下，利用微分不等式理论，讨论了原边值问题激波解的存在性和渐近性态。     

一类随机线性互补问题的求法

考虑一类随机互线性补问题的求解方法,目的是通过定义NCP函数来使正则化期望残差最小化.通过拟蒙洛包洛方法产生一系列观察值并且证得离散近似问题最小值解的聚点就是相应随机线性互补问题的期望残差最小值ERM,同时得到利用ERM到解为有界的充分条件.进一步证明ERM法能够得到具有稳定性和最小灵敏度的稳健解.     

一类拟线性椭圆型方程边值问题的稳定性

在一定条件下证明了一类拟线性椭圆型方程边值问题W~(1,p)(Ω)∩L~∞(Ω)解的存在唯一性,对p≥2及1p≤2两种情形分别在集合收敛与点收敛意义下得到了此类解边值的稳定性.     

On Numerical Solution of Quasilinear Boundary Value Problems with Two Small Parameters

We consider the singular perturbation problem $$-\varepsilon^2u"+\mu b(x,u)u'+c(x,u)=0,u(0),u(1)$$ given with two small parameters $\varepsilon$ and $\mu$ , $\mu =\varepsilon^{1+p},p>0$. The problem is solved numerically by using finite difference schemes on the mesh which is dense in the boundary layers. The convergence uniform in $\varepsilon$ is proved in the discrete $L^1$ norm. Some convergence results are given in the maximum norm as well.     

Shooting Methods for Numerical Solution of Stochastic Boundary-Value Problems

Abstract

In the present investigation, numerical methods are developed for approximate solution of stochastic boundary-value problems. In particular, shooting methods are examined for numerically solving systems of Stratonovich boundary-value problems. It is proved that these methods accurately approximate the solutions of stochastic boundary-value problems. An error analysis of these methods is performed. Computational simulations are given.     

一类拟线性椭圆障碍问题极小正解的存在性

该文使用Ｌｉｏｎｓ的集中紧性原理和变分方法,证明了一类非齐次拟线性椭圆型方程对应的障碍问题中极小正解的存在性．     

一类拟线性奇摄动边值问题的激波性态(英文)

The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.     

Quasilinear Two-Phase Venttsel Problems

A majorant of the Hölder constant is established for solutions of the two-phase quasilinear parabolic or elliptic boundary-value problems with degenerate and nondegenerate Venttsel conditions on an interface. In addition, gradient estimates for solutions of the two-phase quasilinear nondegenerate Venttsel problems are obtained, and the solvability in Sobolev and Hölder spaces is proved. Bibliography: 14 titles.     

Stochastic Method for the Solution of Unconstrained Vector Optimization Problems

We propose a new stochastic algorithm for the solution of unconstrained vector optimization problems, which is based on a special class of stochastic differential equations. An efficient algorithm for the numerical solution of the stochastic differential equation is developed. Interesting properties of the algorithm enable the treatment of problems with a large number of variables. Numerical results are given.     

Shooting Methods for Numerical Solution of Nonlinear Stochastic Boundary-Value Problems

Abstract

In the present investigation, shooting methods are described for numerically solving nonlinear stochastic boundary-value problems. These stochastic shooting methods are analogous to standard shooting methods for numerical solution of ordinary deterministic boundary-value problems. It is shown that the shooting methods provide accurate approximations. An error analysis is performed and computational simulations are described.     

抽象二阶周期边值问题解的存在性

研究了有序Banach空间中二阶周期边值问题解的存在性,利用凸锥理论与上、下解方法,获得了解的存在性结果.     

SICOpt: Solution Approach for Nonlinear Integer Stochastic Programming Problems

We propose a novel solution approach for the class of two-stage nonlinear integer stochastic programming models. These problems are characterized by large scale dimensions, as the number of constraints and variables depend on the number of realizations (scenarios) used to capture the underlying distributions of the random data. In addition, the integrality constraints on the decision variables make the solution process even much more difficult preventing the application of general purpose solvers. The proposed solution approach integrates the branch-and-bound framework with the interior point method. The main advantage of this choice is the effective exploitation of the specific structure exhibited by the different subproblems at each node of the search tree. A specifically designed warm start procedure and an early branching technique improve the overall efficiency. Our contribution is well founded from a theoretical point of view and is characterized by good computational efficiency, without any loss in terms of effectiveness. Some preliminary numerical results, obtained by solving a challenging real-life problem, prove the robustness and the efficiency of the proposed approach.     

Quasilinear Stochastic Hyperbolic Differential Equations with Nondecreasing Coefficient

In this note we prove a result of existence and uniqueness of solutions for a certain class of hyperbolic stochastic differential equations with additive white noise and nondecreasing coefficient. We then show the convergence of Euler's approximation scheme for this equation.     

Quasilinear Parabolic Stochastic Evolution Equations Via Maximal Lp-Regularity

Potential Analysis - We study the Cauchy problem for an abstract quasilinear stochastic parabolic evolution equation on a Banach space driven by a cylindrical Brownian motion. We prove existence...     

一类拟线性椭圆方程边值问题弱解的研究

本文应用上、下解方法和 Leray-Schauder不动点定理 ,证明了一类拟线性椭圆方程边值问题弱解的存在性 ,并且给出了一个应用实例     

Large Deviations for Quasilinear Parabolic Stochastic Partial Differential Equations

Potential Analysis - In this paper, we establish the Freidlin-Wentzell’s large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which...     

m次积分半群的稳定性及相应柯西问题的温和解

首先,对于主算子是m次积分半群的无穷小生成元的一类发展方程引入了温和解的概念,并讨论了温和解与古典解的关系。其次,讨论了m次积分半群的指数稳定性,并给出了两个充要条件。