带移民的非临界分枝相依空间运动超过程

通过对一列带正跳跃的超过程取极限,本文构造了带移民的相依空间运动超过程.在此基础上,利用 Dawson型的Girsanov变换得到了相应的非临界分枝,此变换同时给出依赖于整体状态的空间漂移.     

UNIFORM BLOWUP PROFILES FOR DIFFUSION EQUATIONS WITH NONLOCAL SOURCE AND NONLOCAL BOUNDARY

Long time behavior of solutions to semilinear parabolic equations with nonlocal nonlinear source ut - △u = ∫Ω g(u)dx inΩ× (0, T) and with nonlocal boundary condition u(x, t) = ∫Ω f(x, y)u(y, t)dy on(e) Ω× (0, T) is studied. The authors establish local existence, global existence and nonexistence of solutions and discuss the blowup properties of solutions. Moveover, they derive the uniform blowup estimates for g(s) = sp(p ＞ 1) and g(s) = es under the assumption fΩ f(x, y)dy ＜ 1 for x ∈(e)Ω.     

A LIMIT THEOREM FOR INTERACTING MEASURE-VALUED BRANCHING PROCESSES

1IntroductionItiswellknownthatthe(classical)DW-superprocessiscloselyassociatedwiththe(c1assical)FV-superprocess.Tl1isconnectionisfiIStobservedbyKonnoandShiga(1988),rigorouslyprovedbyEtheridgeandMarch(1991),andgeneralizedbyPerkins(l992).Infact,intermofapproximationofparticlesystemsthisrelationshipisratherintuitive,buttoproveitisnoteasy.I11thispaper,weshallconsiderthesanequestionforthemeasure-valuedprocesseswithinteractions.Forthesakeofbrevity,weomittheintroductionoftl1iskindofmeasure-value…     

A HIGH ORDER ADAPTIVE FINITE ELEMENT METHOD FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS

In this note,we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic p...     

一类具有非局部边界条件的半线性椭圆型方程奇摄动问题

本文研究了一类具有非局部边界条件的奇摄动半线性椭圆型方程边值问题。在适当的条件下，利用比较定理讨论了问题解的渐近性态。     

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.     

KINETIC FLUX VECTOR SPLITTING FOR THE EULER EQUATIONS WITH GENERAL PRESSURE LAWS

This paper attempts to develop kinetic flux vector splitting(KFVS)for the Euler equa-tions with general pressure laws.It is well known that the gas distribution function forthe local equilibrium state plays an important role in the construction of the gas-kineticschemes.To recover the Euler equations with a general equation of state(EOS),a newlocal equilibrium distribution is introduced with two parameters of temperature approx-imation decided uniquely by macroscopic variables.Utilizing the well-known connectionthat the Euler equations of motion are the moments of the Boltzmann equation wheneverthe velocity distribution function is a local equilibrium state,a class of high resolutionMUSCL-type KFVS schemes are presented to approximate the Euler equations of gas dy-namics with a general EOS.The schemes are finally applied to several test problems for ageneral EOS.In comparison with the exact solutions,our schemes give correct location andmore accurate resolution of discontinuities.The extension of our idea to multidimensionalcase is natural.     

基于扰动补偿趋近律的非匹配离散广义准滑模控制

研究了非匹配不确定离散广义系统准滑模控制策略的综合问题.给出了具有前级状态向量的动态切换函数,使得系统能够在切换带内稳定.设计了两种带有扰动补偿的离散广义趋近律,消除了常规滑模控制策略中不确定项必须有界的限制,且不必满足匹配条件.给出了系统准滑动模态保持逐步穿越切换面的必要条件,减小了准滑动模态切换带的带宽.所设计的滑模控制器在有限时间内可达切换面,削弱了系统抖振,有效地改善了系统动态品质.最后,数值算例验证了该控制策略的可行性.     

ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES

We study the long time formation of rarefaction waves appearing in balance laws by means of singular perturbation methods. The balance laws are non standard because they contain a variable u that appears only in the flux terms. We present a concrete example occurring in flow of steam, nitrogen and water in porous media and an abstract example for a class of systems of three equations. In the concrete example the zero-order equations resulting from the expansion yield a type of conservation law system called compositional model in Petroleum Engineering. In this work we show how compositional models originate from physically more fundamental systems of balance laws. Under appropriate conditions, we prove that certain solutions of the system of balance laws decay with time to rarefaction wave solutions in the compositional model originating from the system of balance laws.     

关于非强平稳NA列的重对数律及其应用

本文讨论了非强平稳ＮＡ（ＮｅｙａｔｉｖｅｌｙＡｓｓｏｃｉａｔｅｄ）列的若干重对数律,并用以估计线性模型中ＮＡ误差的方差估计的一类强收敛速度．     

CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME AND STABILITY FOR CONSERVATION LAWS WITH A DISCONTINUOUS SPACE-TIME DEPENDENT FLUX

The authors give the first convergence proof for the Lax-Friedrichs finite differencescheme for non-convex genuinely nonlinear scalar conservation laws of the formu_t f(k(x, t), u)_x = 0,where the coefficient k(x, t) is allowed to be discontinuous along curves in the (x, t)plane. In contrast to most of the existing literature on problems with discontinuouscoefficients, here the convergence proof is not based on the singular mapping approach,but rather on the div-curl lemma (but not the Young measure) and a Lax type en-tropy estimate that is robust with respect to the regularity of k(x, t). Following [14],the authors propose a definition of entropy solution that extends the classical Kruzkovdefinition to the situation where k(x, t) is piecewise Lipschitz continuous in the (x, t)plane, and prove the stability (uniqueness) of such entropy solutions, provided that theflux function satisfies a so-called crossng condition, and that strong traces of the solu-tion exist along the curves where k(x, t) is disco     

GIRSANOV'S THEOREM ON ABSTRACT WIENER SPACES

ＧＩＲＳＡＮＯＶ’ＳＴＨＥＯＲＥＭＯＮＡＢＳＴＲＡＣＴＷＩＥＮＥＲＳＰＡＣＥＳＺＨＡＮＧＹＩＮＮＡＮＡｂｓｔｒａｃｔＬｅｔ（Ｅ，Ｈ，μ）ｂｅａｎａｂｓｔｒａｃｔＷｉｅｎｅｒｓｐａｃｅｉｎｔｈｅｓｅｎｓｅｏｆＬ．Ｇｒｏｓ．Ｉｔｉｓｐｒｏｖｅｄｔｈ...     

HIGH RESOLUTION SCHEMES FOR CONSERVATION LAWS AND CONVECTION-DIFFUSION EQUATIONS WITH VARYING TIME AND SPACE GRIDS

This paper presents a class of high resolution local time step schemes for nonlinear hyperbolic conservation laws and the closely related convection-diffusion equations, by projecting the solution increments of the underlying partial differential equations （PDE） at each local time step. The main advantages are that they are of good consistency, and it is convenient to implement them. The schemes are L^∞ stable, satisfy a cell entropy inequality, and may be extended to the initial boundary value problem of general unsteady PDEs with higher-order spatial derivatives. The high resolution schemes are given by combining the reconstruction technique with a second order TVD Runge-Kutta scheme or a Lax-Wendroff type method, respectively. The schemes are used to solve a linear convection-diffusion equation, the nonlinear inviscid Burgers＇ equation, the one- and two-dimensional compressible Euler equations, and the two-dimensional incompressible Navier-Stokes equations. The numerical results show that the schemes are of higher-order accuracy, and efficient in saving computational cost, especially, for the case of combining the present schemes with the adaptive mesh method [15]. The correct locations of the slow moving or stronger discontinuities are also obtained, although the schemes are slightly nonconservative.     

一个求解多维守恒律方程组的二阶显式有限元格式

１．引言 近年来,在非结构网格上求解双曲型守恒律的数值方法引起了较为广泛的关注,出现了有限体积方法［１］,间断 Ｇａｌｅｒｋｉｎ方法 ［２］,流线扩散方法［３］,以及 ＮＮＤ格式 ［４］等．我们在［６,７］中提出了一种求解双曲型守恒律方程式的有限元方法,它是在一个求解对流扩散问题的有限元方法 ［５］的基础上发展起来的．它是一个显式有限元方法,因此计算量很小．在这个方法中,我们将任意维的问题归结为在单元棱边上的一维计算,引入了积分因子,因此在单元内部可以容纳边界层．这样,它特别适合于对流占优问题以及双曲…     

多维抛物型方程的分支绝对稳定的显式格式

其中及R={0≤x_i≤1,j=1,2,…,p),(?)R只为区域只的边界。 对多维抛物型方程(1)的差分解法,古典显式格式的稳定性条件为r=Δt/(Δx)~2≤1/2p,十分苛刻;古典隐式格式虽是无条件稳定,却需解线性方程组。因此两者的计算量都很大,且它们的精度较低,其局部截断误差仅为O(Δt+(Δx)~2)。因此,对多维抛物型方程而言,构造显式计算、稳定性能良好且精度较高的差分格式便具有十分明显的理论意义和实用价值。本文针对上述古典显式与隐式格式所存在的问题,构造一类对任何p维空间变量的抛物型方程(1)都适用的。分支绝对稳定的显式差分格式,其局部截断误差阶为O((Δt)~2+(Δx)~2),从而避免了解线性代数方程组,大大地减少了计算工作量,且精度较高。 令Δx_k=h_k=Δx=h=1/M(k=1,2,…p)表示空间方向步长,Δt=τ=[T/N]表示时间方向步长,M、N均为正整数。 为简便计,引入下列记号     

非凸双曲守恒律解的渐近性质

本文研究了非凸双曲守恒律ｕｔ＋（ｕ＾３）ｘ＝０解的渐近性态。对于初值具有紧支集或周期函数的情形，我们利用广义特征原理，建立了关于波速总变差的基本递推估计，给出了解的最优衰减速率。     

体积约束的非局部扩散问题的后验误差分析

本文针对体积约束的非局部扩散问题构造了新的后验误差指示器,证明了后验误差指示器的可靠性以及有效性.数值算例验证了理论结果.     

HIGH RESOLUTION SCB SCHEME FOR HYPERBOLIC SYSTEMS OF 2-D CONSERVATION LAWS

1.IntroductionConsidernumericalsolutionsoftheinitialvalueproblemforhyperbolicconservationlawsinonedimensionwhereu~(.ul,u2,...,"m)"andf(u)~(fi(u),fZ(u),',fm(u))".Andconservationlawsintwodimensionswhereu~(ul,u25...,"m)',f(u)~(fi(u),fZ(u),'?fm(u))',andg(u)~(gi(u),gZ(M),',gm(U))".FOrthescalarconservationlawsinonedimension,theTVDconceptbyA.Ha.te.[3]iswidelyacceptedtodesignthenumericalschemesfortheoreticalpurposesandpracticalapplications.Thetotalvariationofagridfunction{uj}denotedbyTV(u)…     

A CLASS OF NONLINEAR NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION

A class of nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series, the boundary layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.