H−1 LSFEM for Fluid‐Structure Problems

The instationary incompressible Navier‐Stokes equations, which appear in the context of a instationary fluid‐structure problem are solved with a Space‐Time LSFEM formulation. Convergence rates of the proposed scheme are examined using the Taylor vortex.     

First Order LSFEM for Second Order Hyperbolic Problems

In the last years the interest in least squares finite element methods has grown due to some interesting properties of these methods (cf. the monographs [1], [2]). While for many elliptic problems the theoretical background has been established, only a few articles analyse least squares methods for transient problems. In this article some new stability estimates for the least squares method for the wave equation in 1 and 2 dimensions are derived. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Space‐Time Finite Elements for Fluid‐Structure Interaction

A numerical method for the analysis of fluid‐structure interaction in the areas of building aeroelasticity and building‐water interaction is presented. In order to achieve optimal convergence of the solution a consistent space‐time discretization and a strong coupling algorithm is applied to the highly nonlinear problem.     

Fully Coupled Fluid‐Structure Interaction using Weak Coupling

We consider the procedure of computing the response of a coupled fluid‐structure interaction problem. Often we have existing software to solve each subproblem separately, and want to couple both. This setting seems to allow only the so‐called weak coupling, which is not sufficient for some problems. We show how to solve the so‐called strong coupling – a totally implicit formulation – by using only the solvers for the subproblems.     

Boundary Value Problems for First Order Stochastic Differential Equations

In this paper, we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition （in the sense of expectation）. Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value. Then by using the contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the existence theorem. Finally, we explain our main results by an elementary example.     

一阶随机微分方程的边值问题

In this paper,we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition (in the sense of expectation).Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value.Then by using the contraction mapping principle and Leray-Schauder fixed point theorem,we obtain the existence theorem.Finally,we explain our main results by an elementary example.     

On Some Inverse Problems for First Order Operator-Differential Equations

Siberian Mathematical Journal - We study solvability of the inverse problems of recovering an unknown function on the nonlinear right-hand side of a first order operator-differential equation in...     

First Order Optimality Conditions for Generalized Semi-Infinite Programming Problems

We study first-order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various well-known constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs takes a weaker form unless a certain constraint qualification is satisfied. In the completely convex case where the objective of the lower-level problem is concave and the constraint functions are quasiconvex, we show that the KKT condition takes a sharper form. The authors thank the anonymous referees for careful reading of the paper and helpful suggestions. The research of the first author was partially supported by NSERC.     

Weak Solutions of Fluid–Solid Interaction Problems

This paper is concerned with various variational formulations for the fluid–solid interaction problems. The basic approach here is a coupling of field and boundary integral equation methods. In particular, Gårding's inequalities are established in appropriate Sobolev spaces for all the formulations. Existence and uniqueness results of the corresponding weak solutions are given under suitable assumptions.     

Cycle‐Continuous Mappings—Order Structure

Given two graphs, a mapping between their edge‐sets is cycle‐continuous , if the preimage of every cycle is a cycle. The motivation for this definition is Jaeger's conjecture that for every bridgeless graph there is a cycle‐continuous mapping to the Petersen graph, which, if solved positively, would imply several other important conjectures (e.g., the Cycle double cover conjecture). Answering a question of DeVos, Ne?et?il, and Raspaud, we prove that there exists an infinite set of graphs with no cycle‐continuous mapping between them. Further extending this result, we show that every countable poset can be represented by graphs and the existence of cycle‐continuous mappings between them.     

一阶时滞差分方程周期边值问题的单调迭代法

该文利用上下解结合单调迭代方法研究了一阶时滞差分方程周期边值问题解的存在性，假设问题的上下解存在，得到两组保证边值问题的极大极小解存在的充分条件.     

Boundary Value Problems for Degenerate Hyperbolic Systems of First Order Equations

In this paper we discuss some boundary value problems for degenerate hyperbolic complex equations of first order in a simply connected domain, in which the boundary value problems include the Riemann-Hilbert problem and the Cauchy problem. We first give the representation of solutions of the boundary value problems for the equations, and then prove the uniqueness and existence of solutions for the problems. In [A.V. Bitsadze (1988). Some Classes of Partial Differential Equations . Gordon and Breach, New York; A.V. Bitsadze and A.N. Nakhushev (1972). Theory of degenerating hyperbolic equations. Dokl. Akad. Nauk, SSSR , 204 , 1289-1291 (Russian); M.H. Protter (1954). The Cauchy problem for a hyperbolic second order equation. Can. J. Math ., 6 , 542-553], the authors discussed some boundary value problems for hyperbolic equations of second order.     

First and Second Order Necessary Conditions for Stochastic Optimal Control Problems

In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.     

含有一阶导数的四阶边值问题正解的存在性

研究了含有一阶导数的四阶边值问题,利用度理论构造出的一个新的不动点定理,由Green函数的性质,给出了一类含有导数的四阶边值问题正解存在的充分条件,得到了边值问题正解存在的一些新结果.     

一阶混合型积分微分方程的周期边值问题

在有一般化的上下解的条件下,研究了一阶混合型积分微分方程的周期边值问题的可解性和最小最大解的存在性。讨论基于迭合度方法,单调迭代方法和新的比较定理。     

一类带一阶差分的离散问题解的存在性

In this paper, we prove the existence of a positive solution and a negative solution for a class of second order difference equations with dependence on the first order difference. Our proofs are based on the Mountain Pass Lemma and iterative methods.     

Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition

Let Ω be a Lipschitz domain in , and be a second‐order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in and of the Neumann problem with data for the operator L on Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operator L to be rough, obeying a certain Carleson condition with small norm. These results complete the results of Dindo?, Petermichl, and Pipher (2007), where the Dirichlet problem was considered under the same assumptions, and Dindo? and Rule (2010), where the regularity and Neumann problems were considered on two‐dimensional domains.© 2016 Wiley Periodicals, Inc.     

一阶常微分方程组周期边值问题的正解

利用锥上的不动点指数研究了一阶非线性常微分方程组的周期边值问题.在某些条件下,证明了上述周期边值问题正解的存在性.     

Banach空间中一阶脉冲微分方程的无穷边值

本文利用Moench不动点定理研究了Banach空间中一类无穷区间上的一阶脉冲微分方程的解的存在性。