A relaxation scheme for conservation laws with a discontinuous coefficient

We study a relaxation scheme of the Jin and Xin type for conservation laws with a flux function that depends discontinuously on the spatial location through a coefficient . If , we show that the relaxation scheme produces a sequence of approximate solutions that converge to a weak solution. The Murat-Tartar compensated compactness method is used to establish convergence. We present numerical experiments with the relaxation scheme, and comparisons are made with a front tracking scheme based on an exact Riemann solver.     

Essential spectra of self-adjoint relations under relatively compact perturbations

This paper is concerned with the stability of essential spectra of self-adjoint relations under relatively compact perturbation in Hilbert spaces. Relationships between relative boundedness and relative compactness of linear relations are established, and some necessary and sufficient conditions of relative compactness and relative boundedness of linear relations are given. It is shown that the essential spectra of self-adjoint relations are invariant under either relatively compact perturbation or a more general perturbation. The results obtained in the present paper generalize the corresponding results for operators to relations, and some of which weaken certain assumptions of the related existing results.     

板几何中具反射边界条件的迁移算子的谱分析

在Lp(1 p<∞)空间上研究了板几何中具反射边界条件下各向异性、连续能量、非均匀介质的迁移方程,证明了该迁移算子产生C0半群的Dyson-Phillips展开式的二阶余项在Lp(1相似文献   

半导体模型中退化漂移-扩散问题解的存在性

研究半导体物理中出现的漂移—扩散模型,这是一个关于带电粒子浓度n,p,静电位ψ的抛物—椭圆耦合方程组,并带有混合初边值条件.对初值在L2+(Ω)时弱解的存在性展开讨论,利用正则化方法和适当的函数变换,使抛物型方程的解具有正下界n,p≥ε>0,同时得到一系列先验估计.然后通过紧性引理和Schauder不动点定理,得到初值在L2+(Ω)时弱解的存在性.     

Drop properties and approximative compactness in Orlicz-Bochner function spaces

The representation of dual spaces of EM(μ,X), owing to its extensive application, is given in this paper. Using the representation, we get the sufficient and necessary conditions of LM(μ,X) possessing drop property, and extend the result of Hudzik and Wang [H. Hudzik, B. Wang, Approximative compactness in Orlicz spaces, J. Approx. Theory 95 (1998) 82-89]. Simultaneously, under some conditions, the weak^∗ drop property in LM(μ,X^∗) and LM^∗(μ,X) is discussed.     

Asymptotic properties of constrained Markov Decision Processes

We present in this paper several asymptotic properties of constrained Markov Decision Processes (MDPs) with a countable state space. We treat both the discounted and the expected average cost, with unbounded cost. We are interested in (1) the convergence of finite horizon MDPs to the infinite horizon MDP, (2) convergence of MDPs with a truncated state space to the problem with infinite state space, (3) convergence of MDPs as the discount factor goes to a limit. In all these cases we establish the convergence of optimal values and policies. Moreover, based on the optimal policy for the limiting problem, we construct policies which are almost optimal for the other (approximating) problems. Based on the convergence of MDPs with a truncated state space to the problem with infinite state space, we show that an optimal stationary policy exists such that the number of randomisations it uses is less or equal to the number of constraints plus one. We finally apply the results to a dynamic scheduling problem.This work was partially supported by the Chateaubriand fellowship from the French embassy in Israel and by the European Grant BRA-QMIPS of CEC DG XIII     

L—Fuzzy拓扑空间中的可数F紧性与几乎可数F紧性

本文在Ｌ－ｕｚｚｙ拓扑空间中引入可数Ｆ紧性与几乎可数Ｆ紧性的概念，并讨论了它们的性质及其相互关系。     

Existence of a solution for a Signorini contact problem for Maxwell-Norton materials

The aim of this article is to study the quasistatic evolutionof a Maxwell–Norton three-dimensional viscoelastic solidwith contact constraints. After introducing the appropiate functionalframework, we will discretize the problem in time using an implicitscheme whose resultant variational inequality is well posed.By using monotonicity arguments together with compensated compactnesstechniques, we will prove that the corresponding discrete solutionconverges to a solution of the continuous problem.     

Banach空间的弱*序列紧性

本文研究了Ｂａｎａｃｈ空间的弱序列紧性．Ｂａｎａｃｈ空间Ｘ称为有（ｗ）性质，如果Ｘ（Ｘ的共轭空间）的每个有界序列有弱收敛子列．我们证明了，如果Ｂａｎａｃｈ空间Ｘ有（ｗ）性质，那么ｌｐ（Ｘ）（１≤ｐ＜＋∞）与ｃ０（Ｘ）也有（ｗ）性质．     

空间l1(Xn)中的弱紧性

本文首先讨论空间l₁(X_n)中的弱收敛性，然后给出了l₁(X_n)中弱紧性的几种等价刻画，同时对l_p(X_n)（１＜ｐ＜∞）中的弱紧性也得到了类似的结果．